But backers of the existing candidates, and many independent observers, have said that favorite-son candidacies are a thing of the past, and that Democratic primary voters would not cede their role to party elders. Current System Assailed

''There haven't been any successful favorite sons since God knows when,'' said William Carrick, campaign manager for Representative Richard A. Gephardt of Missouri. ''It's not going to happen.''

He said state political leaders -Governors, Senators and others -would not risk ''standing on the tracks in front of the freight train of Presidential campaign momentum.''

But Mr. Moynhian, in comments recorded Saturday evening, said that the current system of selecting a nominee was not working.

''Right now, we're letting two of the least Democratic states in the nation, Iowa and New Hampshire, pick our candidate and they then procede to vote against him,'' Mr. Moynihan said.

Mr. Moynihan also said the current system of selecting a nominee had become such a difficult physical and emotional endurance contest that ''no normal person can sustain this.'' He said the system requires so much of candidates that America would be reduced to choosing its Presidents ''from among wise and prudent athletes - a small class.'' Cuomo on His Past

This, he said, made him sympathetic to Mr. Cuomo's decision not to run. ''When you see what these races do to people,'' Mr. Moynihan said, ''I think the Governor has done the right thing.''