It is a peaceful democracy in one of the world's troubled areas, but the tiny Central American nation of Belize suddenly has become a diplomatic hotspot--within Republican Party circles, at least.

Sen. John G. Tower (R-Tex.), chairman of the Senate Armed Services Committee, is at odds with the White House personnel office over which of two Texans should be the first U.S. ambassador to Belize, which gained independence from Great Britain in September, 1981.

The White House reportedly is considering an El Paso optometrist and perennial office seeker, S.L. Abbott, for the post.

Nearly two years ago, however, Tower recommended a Brownsville businessman, Bill Perrin, for the same post. An angry Tower met today with White House personnel chief Helene von Damm to impress on the White House that he still prefers Perrin.

But it is somewhat more complicated than that.

"I was recommended for an ambassadorial appointment by Sen. Tower first in 1970 and then again in 1982," Abbott said today from El Paso. "I frankly don't believe he wouldn't support me. I consider him a friend and political ally."

Adding further to the confusion, Perrin, a longtime political ally of Tower, recently accepted an appointment as head of the Peace Corps in Belize, and is reported to be heading there this weekend.

Abbott, a Republican who made his money selling eyeglasses to the military, was elected to the Texas Legislature in a special election in 1977, but lost the seat in 1978. He ran again two years later and lost again.

Shortly after that, he asked for the help of Texas Republican then-Gov. Bill Clements in gaining a "high-level appointment to the Reagan administration," according to an aide to Clements.

"He did this after losing a seat for the goldarned Texas House," the aide said. "I thought it was kind of pushy. He's kind of a loser."

Several Texas politicians said Abbott, who served as regional director of the Bicentennial Commission for three years, has been lobbying for a government appointment for some time.

"He's offensive to the Republican hierarchy," said one Texas Democrat. "He's a pest. But he's been a Republican for years and years, and he's been very loyal."

"Sen. Tower made a recommendation on behalf of Dr. Abbott to the White House about a year ago--for a non-specified position," said Will Ball, Tower's administrative assistant. " But he feels very strongly that Bill Perrin is the best man for the job. It's accurate to say he would not be pleased if someone were nominated for that job who did not have the qualifications of the man he has recommended."

Republican sources said the recommendation Tower made in behalf of Abbott was "pro forma."

Von Damm could not be reached for comment.

Belize, formerly British Honduras, has a population of 145,000, and is described by one State Department official as one of the "bright spots" of Central America, with beautiful beaches and the largest barrier reef in the Western Hemisphere.

"It's peaceful, it's a functioning democracy," this official said.

The ambassadorship is a somewhat sensitive post, however. British troops still are there, and nearly everyone except the British wants them to remain to provide stability.

Belize borders Guatemala, which is the only nation in the world not to recognize its neighbor, but the two countries are attempting to work out a century-old dispute.

Abbott said today he would welcome the opportunity to serve in Belize. "I've never been there," he said. "It's the kind of place you'd have to be going to to get there. It's on the opposite coast from Acapulco."