Once you get past Jimmy Carter and Charlie Brown, it might be a safe bet that no name appears with more regularity in America's Sunday newspapers than that of Robert C. Byrd.

His is, of course, the majority leader of the U.S. Senate, and there is a good reason for his frequent appearances over the Sunday breakfast table:

Every Saturday the Senate is in session, which tends to be most Saturdays of the year, Byrd holds a press conference.

The West Virginia Democrat, first elected to public office in 1945, has been in politics long enough to know that Saturday is a notoriously dreary news day most of the time.

Reporters and editors lust for snews on Saturdays. Os, since he became majority leader in 1977, Byrd obligingly has been meeting with Washington news gatherers and answering their questions. That is, making Saturday news.

The sessions quickly became one of the city's political mini-institutions. His predecessor, Mike Mansfield (D-Mont.), often met with reporters on Saturdays, but not with Byrd's regularity.

Byrd's counterpart in the House, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), talks to reporters each morning before the House convenes. He puts newsmaking on hold for weekends.

When Byrd began his regular Saturday press sessions, only a half-dozen or so reporters showed up. Since then it has grosn and last Saturday, 24 truned out to question him.

Are these sessions useful?

"Oh, yes," Byrd said. "We get some very good questions and everything is out on the table -- nothing off the record.... I don't think we've missed a Saturday yet when the Senate was in session."

The only difference in Byrd's last coffee klatch was that he was almost 30 minutes late, unusual for a man famed for keeping the Senate's trains running on time.

Once he had shaken all the hands, once the coffee was served in his capacious, chandeliered Capitol conference room, the senator sat down and began.

"I see some new faces here today, but I want to make it clear that only accredited people can be here," he said. "Now, we're off and running."

The questions ranged from his views on a new strategic arms limitation treaty (SALT) and China's invasion of Vietnam to his opinions on the Taiwan issue, the MiddleEast and changes in Senate rules.

His response on each question came in Byrd's usual measured way, often sprinkled with words that ordinary folks don't use much -- "primordial," "countenance," "emanating," and the like.

By the time it was over most reporters had their news story and it would be on many front pages. byrd was calling on President Carter to clarify his thoughts on the SALT II situation.

And by mid-afternoon Saturday the White House was distributing its clarification and once again, on one more Sunday morning, Sen. Robert C. Byrd was being quoted in the newspapers.

Tomorrow, however, the senator won't be quoted on such weighty matters. He has canceled today's press conference so he can go to Nashville, where he will play his mountain fiddle tonight at a national public television fund-raiser.