Remember Grenada? That quiet, sun-drenched Caribbean island became a battleground briefly during the U.S.-led invasion in October 1983. The guns have long been silent, but now tourism is booming.

Last year Grenada had 39,500 visitors, a 22 percent increase over 1983; in the first three months of this year, tourism jumped 32 percent over the same period in 1984. Grenadians, English-speaking and more than 90 percent literate, always have welcomed travelers warmly. But in 1979 a coup removed the island's first prime minister, and from then until the 1983 invasion, increasing Cuban influence put a damper on visits by Americans.

But now the island is drawing more vacationers than it ever has, and the government recently announced these steps aimed at continuing the new momentum and bringing in more needed dollars:

* The first central reservation system for Grenada Hotel Association members has been opened by International Travel & Resorts of New York. By dialing toll-free 800-CALL-GND (or in New York, 212-840-6636), travelers can find out about room availability and make reservations.

* BWIA International has added two direct weekly flights from Miami to Grenada's new Pointe Salines International Airport, making a total of three direct flights a week (one stops at Antigua and St. Lucia, the second at Antigua and St. Martin, and the third at Antigua). The airline has also added connecting service to Carriacou, 23 miles northeast of Grenada (Carriacou and Petit Martinique are the other two islands that make up the small nation within the British Commonwealth). And BWIA is scheduled to inaugurate nonstop Friday service to Grenada from New York's JFK Airport beginning June 28.

* Cruise lines planning to resume service this summer or winter are Royal Caribbean, Sitmar, Epirotiki and Holland America Westours. They will join Paquet, Home Lines, Sun Line, Cunard, Costa and Chandris, which already have begun sailing to the island. Ocean Cruise Lines will visit Grenada next year for its second winter season, while Windjammer Barefoot Cruises (whose Mandalay makes the island one of its home ports) began service last winter and will continue this summer. Royal Viking will make its first stop there next January as part of a world cruise.

* Grenada's government is encouraging the construction of 900 new hotel rooms over the next three years to reach its goal of 1,500 rooms "capable of accommodating 75,000 visitors a year," says George Brizan, minister of tourism. Tax incentives are being offered to foreign investors. But Brizan adds, "we're determined to grow in a limited and tasteful manner." (Government guidelines limit hotel height to three stories -- the height of a coconut palm.)

Five new hotels are scheduled for development, and three resorts will be refurbished. The hotels that are being planned -- all but one by private investors -- are:

-- The 300-acre Grenada Yacht and Golf Club, with an Arnold Palmer-designed course, at Mount Hartman on the south coast. Construction is due to begin soon.

-- A hotel and health club in the northern Levera area, to be opened by American investors.

-- A hotel training school for Grenada students, which would prepare them for jobs in the new hotels by providing actual hotel experience, planned by the government.

-- A hotel on Carriacou, being considered by a German group.

-- A 30-room beach-front hotel, The Bay Resort, being planned by a Grenadian family in the southwestern district of True Blue. Some rooms are expected to be ready for the winter season.

The resorts that are undergoing renovations are:

-- The Blue Horizons Cottage Hotel in Grand Anse, which expects to open at least 10 additional rooms by winter.

-- The Grenada Beach Hotel, which is the island's largest with 184 rooms, where U.S. government personnel have been staying. They have packed up, and most have returned home. The hotel, which is on Grand Anse Beach, will close for refurbishment and is scheduled to reopen this winter.

-- The Cinnamon Hill and Beach Club, the island's first condominium hotel, which is being purchased by American investors. They plan to add 250 rooms.

* Yachting facilities have been improved, and the new Spice Island Marina has opened on the southwest coast.

* The government is developing new attractions for visitors, including the Grand Etang Forest Reserve and Grand Etang Lake, the crater of an extinct volcano. A visitors center is being built, featuring nature trails and exhibits, with funds provided by the Agency for International Development and planning assistance from the Organization of American States and the U.S. National Park Service.

Grenada, at the southern end of the Windward Islands, lies 100 miles north of Venezuela and 12 degrees north of the Equator. Twelve miles wide and 21 miles long, it has 45 white sand beaches.

Information: The Grenada Tourist Department, 141 E. 44th St., New York, N.Y. 10017, (212) 687-9554.

INDIAN CEREMONIAL: One of the largest celebrations of Indian culture in the United States will be held Aug. 8 through 11, when artists, dancers, craftsmen and rodeo cowboys from around the country join in the 64th Inter-Tribal Indian Ceremonial at Gallup, N.M.

Gallup has been the principal trading center for nearby Indian reservations since early in this century, and the ceremonial has enhanced the international reputation of many Indian artists. Their arts and crafts are marketed throughout the year by Gallup's Indian traders. But during this four-day event -- which has been held annually since 1922 -- Acoma, Laguna, Navajo, Zuni and Hopi bring their finest items to be judged by a panel of Indian craftsmen, retired traders, curators from the Museum of Northern Arizona and the Navajo Tribal Museum and professors from the University of Arizona and the University of New Mexico. Last year, the cash prizes totaled nearly $14,000. All entries are offered for sale after the competition ends.

As many as 15 Indian dance groups from Oklahoma to California will perform in the 8,000-seat arena in Red Rock State Park. On Saturday, Aug. 10, downtown Gallup will be filled with the vibrant colors of Indian costumes and the sounds of drums and bells as dancers hold their traditional parade along the streets.

Admission to the grounds at Red Rock is $2 for adults, $1 for children 6 through 11. Tickets for the dance performances are $7 adults, $3 children; for the rodeo, $5 adults, $3 children. Tickets may be ordered by mail and will be either held at the ceremonial office for pickup or mailed directly. (The fees collected are used to finance next year's ceremonial.) Send check or money order (no cash) with instructions to the nonprofit Inter-Tribal Indian Ceremonial Association, P.O. Box 1, Church Rock, N.M. 87311, (505) 863-3896.

Inter-Tribal Indian Ceremonial Association, Indian Country Tourism Council, Gallup-McKinley County Chamber of Commerce, P.O. Box 1305, Gallup, N.M. 87301.

NATIONAL PARK BOOKS: A large selection of National Park Handbooks, formerly for sale only at the individual parks or at the Government Printing Office, is now being stocked by Travel Books Unlimited, 4931 Cordell Ave., Bethesda.

About 100 different titles in the series have been published, although most parks do not carry all the guides, which are priced from $2 to $7. A list of all volumes with GPO order numbers can be obtained from National Park Service, Public Inquiries Office, 1013 Interior Building, Washington, D.C. 20240, (202) 343-4747.