The Reagan administration has won its biggest battle over one of its smallest arms sales of the year -- up to 70 Stinger antiaircraft missiles and 14 launchers worth $7 million for the tiny Persian Gulf sheikdom of Bahrain. But its victory came only after an exhaustive lobbying effort on Capitol Hill and sticky negotiations with Sen. Dennis DeConcini (D-Ariz.), who led the opposition to the sale and exacted his price.

In the end, Defense Secretary Frank C. Carlucci and national security adviser Colin L. Powell struck a deal with DeConcini a week ago allowing Stingers to go to Bahrain under some of the most stringent restrictions and conditions ever imposed on any U.S. arms sale abroad.

Though the deal was cut late last Friday, a last attempt was made to reverse it yesterday by one of the House conferees negotiating the foreign operations section of the omnibus spending bill with his Senate counterparts. The bid was defeated on a 6-to-3 vote among the House conferees, according to DeConcini's office.

In return for his cooperation with the White House, DeConcini has insisted that no other Stingers be sold to any gulf nation and that the administration drop its plan to sell more of the shoulder-fired antiaircraft missiles to the sultan of Oman.

Bahrain had to agree to the same strict U.S.-dictated safeguards over the weapon as those imposed on Saudi Arabia, which has 400 Stingers. The safeguards include separate storage depots for the missiles and the launchers and spot-checks by U.S. officials to assure that all are accounted for.

In a precedent-setting procedure, Bahrain also must pledge to sell its Stingers back to the United States as soon as another U.S. air defense system can be found, but, in any case, no later than 18 months from the date of enactment of the legislation.

In addition, the president must report to Congress every three months about whatever replacement air defense system the White House and Pentagon are proposing. In the future, the president will have to notify the House speaker and Senate majority leader of any offer of Stinger sales abroad.

A State Department spokesman, reflecting the administration's disgruntled resignation to the terms of the deal, said, "There is no possibility of anything better. It is the best we can hope for and at least it will permit us to sell them to Bahrain."

He said Bahrain had agreed to the conditions and that the administration will forward the Stingers "as soon as possible."

The administration had decided to "go to the mat" with Congress, as one White House official put it, because of the importance the administration attaches to Bahrain, which has become the logistical linchpin for the U.S. naval buildup in the gulf.

Technically, the White House does not need to submit an arms sale of less than $14 million to Congress for approval. But the sale of the Stinger to Bahrain had generated so much opposition in Congress that the administration decided to negotiate an agreement anyway.

DeConcini regards the portable, 40-pound Stinger, which has proven to be a deadly weapon against Soviet aircraft in the hands of the U.S.-armed Afghan resistance, as the perfect terrorist weapon for shooting down civilian planes. Many pro-Israeli congressmen view the Stinger sale to Bahrain as an example of America's most sophisticated military technology being transferred to an Arab state.

Administration officials argued that Bahrain has become "a special friend" and that its role in the U.S. gulf buildup had made it especially vulnerable to Iranian threats. Bahrain, they said, had neither the time, money or training to fill the gap in its air defense system with U.S. Hawk, or other antiaircraft missiles, and needed a quick fix immediately.