Mayor Marion Barry once again put off nominating a new chairman for the long-troubled D.C. Board of Elections and Ethics yesterday, citing increased difficulty in finding a qualified candidate who is willing to accept the job.

"I've been turned down by a few more people," said Barry, in explaining why he was unable to meet his latest self-imposed deadline for appointing a replacement for Albert J. Beveridge III, whose term as chairman of the three-member board expired in December.

Beveridge, frustrated by the time it is taking Barry to find a new chairman who is acceptable to the City Council, threatened to quit on Wednesday until Barry assured him that a nominee would be announced this week.

The mayor has discussed the post with lawyer Edward Norton, a former assistant U.S. attorney here and general counsel for the Small Business Administration during the Carter administration. Sources said Norton has also been briefed by Beveridge on the problems of the election board.

Reached at his home last night, Norton said, "I've had conversations with the mayor about that job." He declined further comment.

Beveridge declined yesterday to say what he plans to do, explaining that he wants to confer with the mayor first. "I certainly hope there won't be a snag," he said.

Sources within the council and close to the mayor said yesterday that Barry has been stymied in his efforts by council member William R. Spaulding (D-Ward 5), head of the committee that oversees the elections board. Spaulding, the sources said, is backing a candidate who is unacceptable to the mayor.

Spaulding, chairman of the Government Operations Committee, is urging Barry to nominate Emanuel A. Lipscomb, a lawyer and retired federal official. One source said that Barry doesn't consider Lipscomb to be "chairman material."

Lipscomb, 56, was an assistant director in the Commerce Department's office of textiles from 1964 to 1976 and then was chief of the Census Bureau's foreign trade division from 1976 until last April, when he retired.

He also served as chairman of the D.C. Rent Control Commission in 1975 and 1976 and headed a committee that advised the council on ways to improve the city's error-prone election system.

Lipscomb said yesterday that he last talked to Spaulding about the elections board post two months ago, but added that he is losing interest in the job as time is quickly running out for the board to prepare for the upcoming elections.

"The timing now is getting to the point where . . . if it's delayed much longer, I'd question whether I would accept it," Lipscomb said.

Spaulding was out of town yesterday and could not be reached for comment.

The mayor's long-frustrated effort to find replacements for Beveridge and for Virginia Moye, another board member whose term expired more than a year ago, has kept the board from dealing with a wide range of problems.

Barry nominated former council chairman Sterling Tucker Feb. 23 as board chairman, but Spaulding's committee rejected the nomination March 10. The committee also killed the nomination of Valerie Burden for Moye's seat.

The mayor has not released the names of persons who have turned down the job. Clifford L. Alexander, former secretary of the Army and an unsuccessful candidate for mayor in 1974, had been mentioned by sources, but Alexander took himself out of the running.

William Lewis, acting executive director of the elections board, said yesterday that further delays in finding a new chairman would not pose insurmountable problems in holding elections this year provided Beveridge does not step down before a replacement is appointed.

"If one of the board members were to resign, then it could create problems if the two remaining board members couldn't agree on certain issues," Lewis said.

Lewis said the board, which is trying to overhaul its voter registration system, is capable of holding Board of Education elections in November and, in a pinch, could hold a special September primary election to elect two new Statehood "senators" and a "representative." However, for technical reasons, the board won't be able to hold an election this year of 367 Advisory Neighborhood Commission members.

The board must begin distributing nominating petitions for the September Statehood primary on May 13. Petitions for the November school board elections must go out beginning July 8.