Virginia's rival candidates for governor traded their strongest charges yet today in the final eyeball-to-eyeball confrontation of their campaign, with Republican J. Marshall Coleman telling Democrat Charles S. Robb, "I resent being branded a racist."

As a sharply divided audience of 500 alternately cheered and hissed, Robb shot back that he had ignored so many "distortions, scare tactics and character attacks" from Coleman that "I have run out of cheeks."

"I know what you are up to," Robb said, continuing his not-so-subtle suggestions that it is racist for Coleman to criticize Robb's support of two issues of importance to the state's blacks: the proposed constitutional amendment that would give the District full voting representation in Congress and mail registration of voters.

Robb dismissed as "nonsense and you know it" Coleman's contention that the two issues are tests of the conservative philosophy both men have espoused in the campaign. Robb ticked off a list of conservative Republicans who voted for passage of the D.C. amendment in Congress three years ago: Reps. David Stockman, now Ronald Reagan's director of the Office of Management and Budget, Jack Kemp of New York and Paul Trible of Virginia and Sens. Barry Goldwater of Arizona, Robert Dole of Kansas and Strom Thurmond of South Carolina.

"I'd hardly call those folks left-wingers," Robb said.

Coleman, who four years ago captured about one-third of the black vote in his successful race for attorney general, said it was "outrageous that you can't disagree on an issue without being labeled a racist." He said, "I will compare my record on civil rights with any other official in Virginia, or any other state, including the lieutenant governor."

Seizing another opportunity to link Robb with the policies of his late father-in-law, former President Lyndon B. Johnson, Coleman accused Robb of using "tactics straight out of the 1960s to silence debate."

During a question-and-answer period, Coleman repeatedly refused to say whether he thought his running mate for lieutenant governor, State Sen. Nathan Miller, was guilty of conflicts of interest in proposing legislation designed to benefit clients of his law firm.

Similarly, Robb ducked the question of why he did not include the considerable personal holdings of his wife, Lynda Bird, in the financial disclosure statement he filed with Common Cause.

Minutes after the debate, a new charge of dirty campaigning emerged. Robb campaign spokesman George Stoddard unveiled what he called "the latest Republican dirty trick." Stoddard brandished a brochure which boosts the write-in candidacy of black dissident Cora Tucker. Stoddard denounced the mailing as a Republican effort to blunt Robb's support among blacks.

"We don't know where this came from," said GOP spokesman Neil Cotiaux of the brochure, which stated it had been issued by the "5th District Voters League PAC," although the envelope bore a metered postage stamp of the Republican Party of Virginia.

The Democrats attributed the mailing to Kenneth Klinge, the Republican National Committee operative who came to Richmond a month ago to advise Coleman when polls showed him badly behind. "Ever since Kenny Klinge came in to rescue Marshall Coleman's campaign, he's taken it right to the lowest level of Virginia political history," said Stoddard.

Both candidates were exuberant after the liveliest of all the confrontations between the two men. Each had spent considerable time poking not-so-gentle fun at the other.

Robb twitted Coleman for wearing his political conservatism on his sleeve: "When you constantly have to say, 'I am a true conservative', I say thou protesteth too much," Robb said. Then Robb also noted that Coleman had won the state attorney general's office in 1977 by running as a progressive Republican. "Some of these folks wonder where we've been, Marshall . . . they're looking for philosophical consistency." He said Coleman had been embraced by GOP conservatives and said voters have "a feeling that maybe you've had to sell your soul for that support."

But when Robb blamed a misguided staff member for the "mistakes" in a controversial letter to blacks, Coleman shot back: "If you can't control your staff . . . of 36, how are you going to control state government?"