Budget Director David A. Stockman's proposal for a 20 percent tax on fuel for private and corporate airplanes was shot down last week by a little-known outfit called the Aircraft Owners and Pilots Association.

AOPA has 261,000 pilots as members, and they make an average annual income of $44,000 -- "right in the guts of the Reagan constituency," as one association official said. They are surgeons, dentists, contractors, corporate officials.

"What we had to do was disabuse [the administration] of the notion that everybody in general aviation wears a baseball cap and is called Ace," said John Baker, AOPA's president.

At least 39 members of Congress are pilots (AOPA won't say how many of them belong to the association), and many more depend on small planes during their campaigns. There is, in short, a fairly influential community of interest.

That is not to say there won't be a tax increase on fuel for general aviation, the term that refers to everything that flies except military planes and commercial airliners. The present tax is 7 cents per gallon; the administration is discussing a tax of 12 cents per gallon in the first year and steadily increasing taxes in succeeding years. AOPA is suggesting 8 cents in the first year. Those are details Baker says he has already won the first round.

"They're no longer talking about a percentage tax, where the tax rate would be set" by the Organization of Petroleum Exporting Countries, he said. "We got'em off that. . . . It was apparent to us that they didn't know what they were talking about." With aviation fuel running between $1.70 and $2 per gallon, a 20 percent tax would have added at least 34 cents per gallon.

Over at the Office of Management and Budget, where this all began, there is bemusement.

"All of a sudden the word came down that percentage taxes were absolutely verboten," one official said. "I don't know what happened."

This is not the first one AOPA has won. In 1978, after a jetliner collided with a small plane over San Diego, killing 144 people, the Federal Aviation Administration proposed a major revision of air traffic control rules. The plan would have substantially restricted the right of small planes to fly where they please.

The AOPA labeled the proposal a giant airspace grab, and its members mailed more than 44,000 letters to the FAA. The FAA's appropriations bill on Capitol Hill mysteriously got lost in committee, then emerged after the FAA had agreed to withdraw almost all of its proposed rules.

"We didn't have time for letter writing" on the tax proposal, Baker said, "so we made a few telephone calls."

AOPA's $40 million annual budget has been adequate to pay for programming a computer with the names of association members who can call a member of Congress by the first name. Some didn't have to be called.

For example, Rep. Norman Y. Mineta (D-Calif.), who is not a pilot but is the chairman of the House Public Works and Transportation aviation subcommittee, immediately issued a statement opposing a 20 percent tax. "We thought the administration had made a typographical error when we saw that 20 percent," a staffer said.

The underlying issue is one of aviation's oldest running controversies: who should pay how much for the maintenance of the vast governmental structure that aids aviation, from air traffic control to electronic navigation aids to weather information.

The general taxpayer is picking up much of the tab these days, and it is the Reagan administration's intention to shift about 85 percent of the bill to the users: either the commercial airliners or the general aviation community.

The remaining 15 percent still would be charged to the general taxpayer as a contribution to the burden military aviation puts on the system.

There are various estimates, but the one the OMB is using says that general aviation requires 25 percent of the FAA budget of $3.3 billion, but pays only 10 percent.

Naturally, the AOPA contests that view. "There are 220,000 airplanes," said Baker, "and only about 6,000 of them are jets or turboprops," the kind of high-performance aircraft that require air traffic control service.

The rest, he said, are used primarily for personal transportation. "We move more people than the combined totals of 21 of the 31 largest airlines."

Transportation Secretary Drew Lewis said in an interview that the final administration aviation tax package has not been nailed down, but that a review of the 20 percent proposal plus the once-proposed 9 percent ticket tax for commercial airline passengers would have generated substantially more revenue than the FAA needed.

The AOPA, he said, never talked to him. Lewis is a pilot.