Belize has come up in the world since a long ago travel writer told readers of Holiday magazine: "You could be excused for believing that Somerset Maugham invented it."

Nowadays, Belize (formerly British Honduras) is a full-fledged country with matching problems, and you also might be excused for believing that somebody like filmmaker Francis Ford Coppola invented it. He hasn't yet done so, but the way Central America works, stranger things could happen.

Both Coppola, who owns property in Belize, and Prime Minister George C. Price, who led efforts for Belizean independence, are coming to town this week to talk about the tiny democracy whose police carry "bobby" sticks instead of guns, whose barrier reef is described as the most beautiful in the Western Hemisphere and whose Mayan ruins haven't come anywhere near being totally catalogued.

The Price-Reagan conversation at the White House is expected to get around to the threat posed by $6 million worth of U.S. military equipment that the administration cleared earlier this year for Guatemala. One of the stickier aspects is that Guatemala doesn't recognize Belize. As a peace offering, perhaps, Belize wants to give Guatemala 10 acres so it can build an embassy in the Belizean capital of Belmopan. Guatemala, which wants the whole country, isn't interested.

Coppola's presence here won't have anything to do with apocalyptic showdowns or with Hollywood-style socializing. As one who has been talking about training young Belizeans in the technology of filmmaking, he's drumming up interest in the potential offered by English-speaking Belize to American investors.

His Thursday night dinner will enable U.S. businessmen to meet Price, several of his cabinet ministers and Belizean businessmen in the official party. Coppola's other guests are coming from Capitol Hill, the State Department, the Peace Corps, the World Bank and the British business community. Britain still has troops in Belize for what has been described as "an appropriate period of time."

Price will dine with Vice President Bush tomorrow night, have breakfast Thursday with a group on the Hill and be honored by his own embassy Friday night. The visit will provide the White House a chance to remind everybody that it considers Belize a peaceful corner in an otherwise turbulent area and the administration is providing support and assistance accordingly.

Or as the Belize desk officer at the State Department, Cynthia Thomas, summed up the first two years of Belizean independence: "It's been a pleasure to come to work every single day. Who else in the office of Central American affairs can say that?"