Lawyers for Dean G. Skelos, the former New York Senate majority leader, and his son, Adam B. Skelos, who were convicted of all eight bribery, extortion and conspiracy counts against them in December, asked a judge on Wednesday to let them avoid prison and be sentenced to perform community service.

The requests by Mr. Skelos, 68, a Republican from Long Island who forfeited his Senate seat upon his conviction, and his son, 33, come less than a month before both are to be sentenced on April 13 for their convictions in one of the two most prominent public corruption trials to be held in New York City in decades.

The other trial was of Sheldon Silver, the former State Assembly speaker, who was convicted of corruption charges on Nov. 30. He is to be sentenced on the same day by a different judge, also in a federal courthouse in Manhattan.

Mr. Skelos and Mr. Silver, a Manhattan Democrat, were once among the most powerful leaders in the state. Their trials, which exposed influence peddling and other forms of corruption in Albany, seemed to put the capital’s culture itself on trial.