Virginia Republicans today acclaimed Rep. Paul S. Trible Jr. their candidate for the U.S. Senate, warning incumbent independent Sen. Harry F. Byrd Jr. that he should not try to prolong his reign over a seat the Byrd family has held since 1933.

Trible, a 35-year-old member of Congress from Newport News, campaigned and jockeyed for position for more than a year to assure his nomination without opposition. His triumph was overshadowed, however, by increasing speculation that Byrd would cancel his planned retirement and turn the November election into a volatile, three-way race.

After several days of internal debate about how harshly to respond to the possibility of a Byrd candidacy, the Trible campaign chose former Democrat Herbert H. Bateman to send a message to the revered 67-year-old senator and his friends who are currently urging him to remain in Congress. Bateman, a Republican candidate for Congress and an old friend of the Byrd organization, said a three-way race would divide the state's conservative vote and help assure the election of a Democrat.

"The events of the past fortnight can only play into the hands of liberals who have become wilder and wilder," Bateman said. The audience erupted in laughter and applause as most of the delegates interpreted his remark as a play on the name of state Sen. L. Douglas Wilder, a Democratic power broker who is anathema to many Republicans. "This effort is not one that bodes well for our senior senator," Bateman said.

Trible in his acceptance speech made no reference to Byrd, but called on Republicans from President Reagan to Sen. John W. Warner to show that the GOP would enthusiastically support him even if Byrd, who usually votes with the Senate's Republicans, chooses to run.

Trible, wearing a navy blue pin-striped suit, white shirt and red tie, promised the 3,000 delegates in the Richmond Coliseum to uphold "the time-honored conservative principles" of balanced budgets, limited government and strong defense, long the cornerstones of Virginia politics.

"Our purpose is not to save free enterprise but to free enterprise so that together we can save America," said Trible, who was flanked by his wife Rosemary, winner of the Junior Miss beauty pageant in 1967, and their two young children. "I believe we can achieve economic recovery by adhering to our Virginia traditions."

While he didn't mention Byrd or his Democratic opponent, Lt. Gov. Richard J. Davis, Trible told the crowd that the Republicans are "a united and well-organized party, dedicated to principle and confident of victory."

Even so, his campaign was unable to stage a unity press conference with the state's entire Republican congressional delegation during the two-day gathering, as jittery fellow Republicans shied away from a direct challenge to Byrd, a politician whom many Virginians regard as a legend.

Southside Virginia Rep. Robert W. Daniel Jr. said he turned down an invitation to appear with Trible at a unity press conference yesterday because "I had work to do in Washington." And Rep. J. Kenneth Robinson, who lives in Byrd's hometown of Winchester, and like Daniel, depends on the votes of conservative Byrd Democrats, did not attend the convention.

"Kenny Robinson will support the Republican nominee, I'm sure," said Norfolk Rep. G. William Whitehurst of Virginia Beach, Trible's political mentor and a key campaign official. "It's going to cause him some heartburn." Robinson could not be reached for comment, but an aide said the congressman's absence was not related to the draft-Byrd movement and affirmed that Robinson would support Trible.

As the Republican convention ended early this afternoon, Byrd's closest political allies were in their offices around the state collecting the completed petitions that must be submitted by Tuesday to make the senator an official candidate in November. Two of the draft-Byrd leaders, former state Del. W. Roy Smith and J. Smith Ferebee, said they had collected more than the required 10,700 signatures.

"He's concerned about what's the best thing to do and about the national and international situation," said Ferebee, who said he spoke with Byrd yesterday. "The people who are accusing him of breaking his word haven't taken that into consideration."

Eight years ago Trible was a prosecutor in rural Essex County (population, 9,000) where his family has lived for generations. Through a combination of persistence, hard work and good luck, Trible was elected to represent the previously Democratic 1st District in the House of Representatives at the age of 29, and has been reelected twice by increasingly wide margins.

Shortly after his last election Trible began travelling around the state, positioning himself to run for Senate in case Byrd retired. Trible was careful to avoid the appearance that he was trying to push Byrd out, but when Byrd decided to retire other Republicans found Trible had the nomination locked up.

In order to do that, Trible had to curry favor with the conservative establishment that has long guided Virginia politics and anointed its candidates. Many of that group are now backing him, but others have remained suspicious of his youth, ambition and the fact that he was not their hand-picked candidate.

"I'm obviously young -- I'm 35 -- and I'm obviously ambitious," he said in an interview this week. "Ambition is not a bad word in my vocabulary. In fact, it's the stuff that made America great."

Trible said his main goal will be to increase his name recognition around the state. He has projected a budget of $2.8 million for the campaign and has raised nearly $400,000 so far, with another $300,000 promised by the national Republican Party affiliates.

His campaign plans to counteract the image of youth by stressing his experience in Congress and his service on the House Budget and Armed Services committees. "He'll require no on-the-job training, as will the man from Roanoke," said Warner, referring to the nominee of the Democratic convention there.

Trible also remains a staunch defender of the administration's economic policies, a strategy some members of his own party say could boomerang if the economy does not improve before November. Campaign strategists said Reagan remains personally popular in Virginia, and Trible disputes the theory that Republican J. Marshall Coleman lost the 1981 gubernatorial election because he had wrapped himself too tightly in Reagan's mantle.

"I think it was a commentary on the candidates of 1981," Trible said, "and the Republican Party still far better represents the thoughts and aspirations of the people of Virginia."