The fragile political coalition that elected Virginia Gov. Charles S. Robb is being tested again amid an intense lobbying campaign over the filling of a vacancy on the seven-member State Supreme Court.

Blacks and women have put forth candidates, urging Robb to become the first governor to open up the all-white, all-male court. But Robb also has been hearing from his supporters in the state's old guard, many of whom are urging him to stick with tradition and name a conservative ex-state senator who is now a judge in Cheseapeake.

The names of still more candidates have circulated in recent weeks, including that of former state attorney general Andrew P. Miller, now a lawyer living in Alexandria. Miller said Friday that he had "absolutely no comment" on the reports.

"People are bombarding the governor with mail and visits on behalf of all kinds of candidates," said Del. Thomas Forehand (D-Chesapeake), whose personal choice, Circuit Court Judge William Hodges, a former state senator, has been pushed by former Rep. Watkins Abbitt and other leading conservatives.

The appointment, expected to be announced this week, was tossed to Robb in late February when the General Assembly adjourned after deadlocking on a replacement for Judge W. Carrington Thompson of Chatham in Southside Virginia, who retired March 2.

It was the first time in recent years that Democrats, who control judicial selections in the state through bloc voting, failed to settle on a choice for the high court, one of the party's choice political plums. Under the constitution, Robb can make an interim appointment, to be ratified by legislators at their next session.

Many lawmakers argue that the vacancy has given the governor an unexpected opportunity to reach out beyond the typical pool of judicial candidates in Virginia.

"The governor is in an interesting situation in that he can go beyond the legislature's usual choices," said Del. James Almand (D-Arlington). "It's a great opportunity, which I suspect is why he is taking his time."

From the outset, Robb insisted that he was starting with a "clean slate." He told reporters early in March that the legislature's two candidates--Hodges and Richmond Circuit Court Judge Marvin Cole--would have no special advantage. Nor, he said, would he be "intimidated" by any political faction.

The lobbying over the appointment is an example of the pressures that Robb has been under since he was swept into office with the backing of a disparate coalition of blacks, liberals and key members of the state's old Democratic organization, since turned independent.

Some supporters question whether Robb has not bought himself trouble with his typically cautious and deliberate handling of the issue.

"If I'd been him, I'd have done it right away and let us find out about it on the radio, driving home from the session," said one legislator. "Then he wouldn't have allowed so much pressure to build, and had so many people to disappoint."

Black leaders were among the first to come forward with their own nominee, Archie Elliott, a general district court judge from Portsmouth. Elliott, a former city councilman, emerged as the choice of the state NAACP and the Old Domininion Bar Association, a predominately black lawyers' organization.

Last week a coalition of women's groups lobbied Robb, urging the appointment of Dulcey Fowler, senior staff counsel for the U.S. Fourth District Court of Appeals in Richmond, the candidate proposed by the Virginia Women Attorneys Association.

Amid all the pressure, Robb systematically has been reviewing a field of more than 30 potential candidates, asking for resumes, writing samples and other proof of judicial qualifications.

"The governor has really insisted on a broad search," said Timothy Sullivan, a Robb aide. "Legal qualifications are the most important. What he is looking for is a person who is going to make a major additon to the court."

Lawyers, particularly in Northern Virginia, long have argued that the Virginia Supreme Court, typically conservative in its decisions, has lacked the depth of other state supreme courts and could use the addition of someone with strong analytical or scholarly skills.

Still, in a state where there are only seven blacks and five women among 284 lower court judges--numbers that reflect only a slight improvement since 1973, when there were no blacks and only two women in the state judiciary--some argue that the governor should make a special case for greater representation on the bench.

"I think this is an opportunity for the governor to broaden the court in terms of race, or sex or both," said Sen. Joseph V. Gartlan (D-Fairfax). "I would hope, if he can find a qualified candidate in those categories, he would nominate that person."