As a measure of its unhappiness with the government of this island state, the Carter administration has not allowed its ambassador, stationed in nearby Barbados with responsibility for a 10-island area, to visit here since before Christmas.

In the words of an administration official in Washington, the United States is trying to send a disapproving message to Grenada by keeping it "at arm's length [and] distancing outselves" from it.

On its own, Grenada's People's Revolutionary Government, which seized power in a March 1979 coup, could hardly be more distant. At every opportunity, at home and abroad, its representatives denounce U.S. policy on everything from Afghanistan to Zimbabwe.

But the real sore point between the two is Grenada's close relationship with Cuba, something this tiny country -- population 110,000 -- flaunts before its massive northern neighbor like a brave mouse teasing an enraged but tightly leashed lion.

Not only has Grenada developed strong diplomatic and technical links with Cuba, but its newly formed army has been helped by Cuban advisers and, the United States believes, Cuban-supplied arms. Cuban President Fidel Castro is regularly lauded in Grenadian government speechs and Prime Minister Maurice Bishop has compared the coup that brought him to power to "a successful Moncada," a reference to Castro's unsuccessful 1953 assault on a Cuban Army barracks that marked the spiritual beginning of the Cuban revolution.

According to officials in the State Department and regional governments here, little evidence exists to support charges in Washington and the Caribbean press that Cuban troops are training guerrilla fighters from other countries in the Grenada mountains. The battle for influence in the islands is still a far cry from the full-blown war of real bullets across the Caribbean in Central America.

But it is a battle nonetheless, and one that the United States appears still not to have decided how to fight as it struggles to deal with its smallest hemispheric neighbors. So far, it has opted for a combined policy of military "containment," promised economic aid and diplomatic pressure in the form of spelling out the benefits of U.S. friendship and the liabilities of close relationship with Cuba.

The last time Washington felt itself seriously threatened by Cuba in the Caribbean was in the Dominican Republic in 1965. At that time, the mere suspicion of communist influence inside a broad-based movement to reinstall outsted constitutional president Juan Bosch was enough to justify the intervention of 25,000 U.S. troops to prevent his return to power.

Although the priorities of the current U.S. administration have changed somewhat from those of President Lyndon Johnson, the United States had continued to exert strong leverage in the Dominican Republic, perhaps its closest ally in the Caribbean. In May 1978, the Carter administration was committed to promoting free and fair elections there. When three-term president Joaquin Balaguer saw he was badly losing an election to his opposition and sent out troops to seize the ballot boxes, U.S. disapproval was quickly and sharply voiced.

Perhaps even more, ominous, however, from Balaguer's position and that of his armed forces, was the pointed visit to Santo Domingo of U.S. Army Southern Command commander Gen. William McAuliffe, whose photograph beside opposition candidate Antonio Guzman was prominently displayed in Dominican newspaper. The message was unmistakable in a country for which the U.S. military intervention seems like yesterday.Balaguer acquiesced, the vote-counting went on, and Guzman won handily. The high-powered U.S. delegation to his inauguration the following August included then-secretary of state Cyrus Vance and United Nations ambassador Andrew Young.

By the standards that permitted authorization of the 1965 intervention in the Dominican Republic, as well as the strong pressure in 1978, the current situation in Grenada is intolerably threatening to U.S. interests.

But there is a consensus among U.S. policy-makers that a similar intervention in 1980, even if it could be justified at home, would not be acceptable to the rest of the world and would provide only a short-term solution to problems in the islands.

In Grenada, in fact, pressure seems to have had the opposite of the effect desired. U.S. relations with the island have gone from bad to worse as the other. The U.S. response has been the sort of diplomatic stonewalling implied in the State Department's refusal to allow its ambassador to visit Grenada, something that the embassy itself has protested as counterproductive.

Both the hard- and soft-line views on what to do about Cuba in the Caribbean have their advocates within the administration. The Pentagon and intelligence officials have argued that the situation calls for a military response, what Jamaican opposition leader Edward Seaga calls "a tangible expression that the line would be drawn somewhere." The example of Grenada, and administration official said in Washington, "has made us realize how vulnerable the islands are. All it takes is a small armed group to install a very distasteful government."

Reaction to the Grenadian coup in the region itself was a continues to be varied. Trinadadian Prime Minister Eric Williams, who is not known for smooth diplomacy, continues to refuse to talk to the new leaders on the neighboring island and has ostentatiously thrown Bishop's letters to him unopened into the trash can.

In Barbados, an island well known for its own conservative politics, there is a certain discomfort with Grenadian policies but a basic understanding of their antecedents. "The [previous] government there was repressive, and there was a definite silence about it from both the world and the region," a senior Barbados Foreign Ministry official said. "It's still against the tradition we would like to see here, but I'm not surprised at it."

This official and others warn that both internal Grenadia politics and Cuba's own strategies and goals for the region call for a more sophisticated U.S. response than has been forthcoming so far.

They note that the Grenadian situation is unique in the level of direct Cuban involvement there, and growing Cuban influence overall in the Caribbean appears to be much more subtle and gradual. It is a question of waiting patiently for and seizing opportunities as they present themselves.

In Jamaica, Cuba has demonstrated its appreciation for the friendship of Prime Minister Michael Manley and shown its interest in the increasingly strident level of political and ideological debate by replacing its former low-profile ambassador there with Ulises Estrada. He is an experienced political operative who has held high-level positions within the Communist Party Central Committee's American Affairs Bureau and who is also, according to Carter administration sources, an officer in the Cuban intelligence service.

In other island nations that have maintained at least cordial relationships with Cuba, contacts with students and labor groups have been increased, as well as offers of free education in Cuba. Sympathetic political parties, albeit small in size and number for the moment, are given aid and encouragement. The Cubans also pay attention to details such as providing printing presses and supplies of paper for the parties to print their broadsheets.

Whenever possible, Cuba makes use of aid to the islands in the forms that are cheapest and most plentiful -- manpower and equipment. In Jamaica, hundreds of Cuban construction workers are building low-cost housing. In Grenada, 250 laborers are building an airport with Cuban bulldozers and money contributed by sympathetic Arab states and locally sold bonds.

The United States and political opponents of both these governments believe that these projects are mere ruses to station large numbers of Cubans on the islands. They say these Cubans are in charge of infiltration and training ideological cadres. Particularly in the case of the Grenadian airport, U.S. officials have voiced strong suspicion that the project will soon be put to military use by the Cubans, perhaps as a stopover point for troops destined for Africa.

"The runway is long enough for any existing plane," an administration official said in explaining U.S. suspicious. "And who is going to fly there? You're not going to get 747s landing in Grenada; they don't have the hotel space for that many people." The conclusion is that the runway is for Cuban military planes.

Yet here in St. George's, even the business community, which has its own strong doubts about the group of young leftists that has seized such tight control of the island, is pleased about the new airport. The businessmen consider it a "pity," in the words of former Grenadian Chamber of Commerce president Geoffry Thompson, "That the Americans or the British did not seize that initiative" and build it themselves.

"Sure, Cuba is not going to put it in without expecting a quid pro quo. Look at the airports in Trinidad, in Antigua and Barbados -- the Americans built them and their military planes put down there every day. If they would have built this one, they would have expected the same thing." His concern is not that the U.S. worry over Cuba is unjustified, but that in its preoccupation with the trees -- the housing projects and the airports -- the United States is not seeing the forest of Cuban involvement and taking measures to counter it on its own terms.

The way Thompson and others like him here see it, the Grenadian tourist industry, one of the island's principal money-earners, has suffered because incoming foreigners must stay overnight in Barbados to switch to the small, two-engine propeller craft that are the biggest Grenada's current airport can accommodate. Many times, the tourists simply decide that a Barbados vacation is less trouble and skip Grenada altogether. With the new airport, and planned expansions in tourist hotels, Grenada hopes that 747s will indeed land here some day, and it expects to be ready for them.

Asked about U.S. concerns that the airport is "too big' to be anything other than a planned Cuban military installation, Thompson said the situation was "quite the contrary. . . . Tourism is the only industry here that can expand quickly enough to create new jobs," and solving Grenada's severe unemployment problem is one of the few ways he and other concerned Grenadians can see to lessen the excuses for increased government authoritarianism and ever-closer relations with Cuba.

Even ostensibly close U.S. friends in the region argue that the United States, in its zeal to nip perceived Cuban expansionism in the bud, is not taking advantage of the sometimes small ways it could improve relations with the islands. A number of Caribbean governments, for example noted that in Carter's nationwide speech last Oct. 1 the U.S. response to the presence of Soviet "advanturism" was given without any prior consultation with the island governments themselves, or even regional U.S. embassies.

Relations with Barbados, perhaps the most stable U.S. ally among the small former British colonies, are given as another example of perceived U.S "insensitivity." Although Barbadian officials say relations have "improved over the past two years", there remains a residue of bad feeling over the existance there of a secret U.S. Navy submarine monitoring station on land leased under treaty with the former colonial power in 1956.

While not an issue in the United States, protracted negotiations over the base dominated Barbados' view of Washington for years. Under the treaty with the British, a high-level Barbados official said, "The United States has an obligation to provide us with naval training and pay rent. They never paid a cent, not even for the use of our roads or our facilities. We wanted to know what they were doing there; we wanted back payment" for all the years 60 sailors were stationed at the facility, called the St. Lucy Naval Base.

When the treaty expired Barbados first demanded $200 million in back and future payments, according to diplomatic sources. While the United States felt that amount ectravagant, its counteroffer was only $250,000, a figure even U.S. officials now agree was an insult. Last year, the United States abruptly canceled the negotiations and pulled out, saying that "new technology" had given it similar monitoring capability on its own shores, and it no longer needed Barbados' services.

"We say we threw them out, and they say they left," the Barbados official said.

While the island government give the United States high marks for quick and generous disaster assistance in the case of hurricanes and volcanoes, many of them, not surprisingly, believe that U.S. economic assistance is too meager. They object to an emphasis on regional, rather than bilateral aid, that sends the bulk of U.S. money to a very few countries and the rest into a regional bank whose priorities are said to be antiquated and whose disbursement is slow.

U.S. officials in the region admit that, despite the conclusion of numerous of their own studies that the war for influence and the continuance of democracy in the Caribbean are to be won by helping alleviate the region's severe economic problems, the Carter administration has limited its aid and focused it on countries that already align their foreign policies closet to those of the United States.

Thus, more than half of the $149 million the administration has requested for economic assistance in the Caribbean during 1981 is destined for bilateral programs in the Dominican Republic and Haiti, both of which have fairly consistently supported U.S. policy initiatives in forums such as the United Nations even when it means going against most of the rest of the Third World.

Caribbean officials repeatedly cite the United States' own version of its policy toward the region -- a five-point program that includes "significant support for economic development; firm commitment to democratic practices and human rights; clear acceptance of ideological pluralism; unequivocal respect for national sovereignty; and strong encouragement of regional cooperation and of an active Caribbean role in world affairs."

They cite speeches like President Carter's last Nov. 28 when he noted that "economic deprivation creates vulnerabilities to extremism and to foreign intervention," and argue that real economic help means more than foreign aid programs.

"We need preferential tariffs and preferential incentives," argued Jamaica's Seaga on perhaps the one point where he and Manley appear to agree. "It's more than bilateral programs. We're only 900 miles away from U.S. ports, yet we don't do business with the United States. Tell us what you want to buy, and we'll produce it; We've been doing the same things since the 1940s, and it hasn't reduced unemployment at all.

"Your problem is that you always thought this was just a nice resort area. What could happen here? Well, it's not just a bunch of beaches; it's a bunch of countries."