For the second time in recent months, Labor Secretary Raymond J. Donovan has tried without success to get White House approval for his candidate for a federal judgeship in New Jersey over objections of Republican Gov. Thomas H. Kean.

Last time, Donovan's efforts were blocked by top White House officials. This time, the effort collapsed of its own weight, with even Donovan's allies in the administration, including presidential personnel chief Helene von Damm, refusing to go along.

The major reason was that Donovan attempted to fill the judgeship with one of Kean's political appointees--and did not tell the governor about it in advance, administration and Republican Party sources said yesterday.

Donovan last tried to pick a New Jersey federal judge in September over protests of Kean and then-Sen. Nicholas Brady, a Republican. Both complained that Donovan was violating Senate tradition, which dictates that the senior senator from the president's party--then Brady--makes such recommendations to the White House.

Last year, after a special prosecutor twice found "insufficent credible evidence" to sustain allegations that Donovan had associated with organized crime figures, Reagan made it clear that he considered Donovan vindicated. But some senior White House officials, including chief of staff James A. Baker III, let it be known they would like Donovan ousted from the Cabinet.

When Donovan's choice for the judgeship came before a White House judicial selection committee, it was set aside.

The November election left New Jersey without a GOP senator, as Democrat Frank R. Lautenberg was elected to join Sen. Bill Bradley.

When a federal judge in Trenton resigned from the bench recently, Kean recommended Maryanne Trump Barry, a first assistant U.S. attorney in Newark. Her brother is Donald Trump, a New York condominium and Atlantic City hotel developer and Reagan campaign contributor.

Once again, Donovan and a political associate, New Jersey lawyer Thomas H. Bruinooge, who worked with Donovan during the 1980 Reagan campaign, sent the White House their choice for the seat, administration and GOP sources said.

Donovan picked Joseph H. Rodriguez, New Jersey's "public advocate," or public defender, a conservative Democrat who had worked for the Kean campaign, and was appointed to his current post by Kean.

This irked Kean, a moderate Republican who won a narrow 1981 victory after Reagan campaigned for him. A source close to the governor said Kean felt Donovan was trying to embarrass him by offering one of his appointees--one who Kean values--as a rival to Kean's candidate for the judgeship.

Donovan, on the other hand, was a leading fund-raiser for Reagan in the 1980 campaign, and has sought to control patronage in his home state. He was unavailable for comment yesterday. But other administration sources said Donovan recently called von Damm, with whom he also worked in the 1980 campaign, to push his candidate, Rodriguez.

Aides to Bradley said the senior Democratic senator was "consulted" by Kean but did not endorse his choice because he wanted to avoid getting caught in a dispute between the governor and Donovan.

This week, Von Damm contacted Kean, and learned that Donovan's choice was a Kean appointee. Kean reportedly complained to her that he had not been informed in advance of Donovan's recommendation, and insisted that he not lose one of his appointees, an administration official said.

Von Damm then recommended Kean's choice for the job--Barry--to the White House judicial selection committee, the official said.