Coleman Young had some words of advice for his fellow big-city mayors as they meet in Washington this week. "I've been telling them the train is leaving and there are very few tickets left," he said yesterday. "And after New Hampshire there aren't going to be any left."

Young, the Detroit mayor, was talking about Democratic presidential politics. "And I was only half kidding," he said with a wide grin.

Actually Young, long one of President Carter's staunchest supporters, had little selling to do at the U.S. Conference of Mayors meeting, only two years ago the site of widespread complaints about the Carter administration. They all knew Carter defeated Sen. Edward Kennedy (D-Mass.) by a 2-to-1 ration n the Iowa precinct caucuses.

Chicago's Jane Byrne, Kennedy's best known supporter among the mayors, didn't attend the meeting. And it was hard to find a pro-Kennedy mayor anywhere. "If there are any here, they aren't speaking up very loudly," said Young. "The only person I could identify as pro-Kennedy here is Mayor Fulton."

Nashville's silver-haired mayor, Richard Fulton, was keeping a decidely low political profile. "Sen. Kennedy is still a viable candidate, but just barely,"Fulton said. "He must have substantial wins in both New Hampshire and Maine to regain the support he's lost."

As political animals, mayors like to be with a winner.It helps them back home and they think it helps them deal with the federal bureaucracy.

But beyond that mayors feel the Carter administration, after an uncertain start, has delivered for them. Last June, the U.S. Conference of Mayors strongly endorsed Carter's urban and energy programs. And when they met with the president and a host of administration officials Thursday and yesterday, it was more a love feast than a gathering of potential adversaries.

"There is no question in my mind that the Carter administration has done more than any other administration in history for the cities of this country," St. Louis Mayor James Conway declared.

It was difficult to find a disparaging word even among Republicans. "My reaction is very, very positive," said Indianapolis Mayor William Hudnut III. "I'm glad to find the president isn't trying to balance his budget on the backs of the cities."

"Frankly, I have to be positive about the president," said Richard Berkley, the new Republican mayor of Kansas City, Mo. "In Kansas City, we've been the beneficiary of some very timely help since I've been mayor."

It wasn't this way two years ago. At that time, mayors were complaining about the sparsity of Carter's urban budget. "Mayors all over the country are alarmed over the economic philosophy reflected in President Carter's budget," Syracuse Mayor Lee Alexander said at the time.

This week Alexander was smugly telling reporters he was glad he endorsed Carter last fall. "I decided when it was tough. Now it's easy to endorse him," Alexander said. "It's tough to run against a wartime president and that's what we've got now."

The only serious criticism that the administration came under was over inflation.Carter conceded "the most serious domestic problem is still inflation."

"There is no way we can spend our way out of inflation," the president said. "There is no way we can wish our way out of inflation. There is no way we can complain our way out of inflation. The only way we can do it is to work our way out."