Almost every governor of New York has been mentioned as a potential presidential candidate, and Hugh Carey was no exception. When he was still a Congressman, the first *Almanac of American Politics* (in 1971) described him (p. 536) as "one of the few remaining New York politicians who can win Irish working-class votes and who at the same time possesses a liberal voting record." In the 1974 gubernatorial race, he easily defeated Malcolm Wilson (Nelson Rockefeller's conservative lieutenant governor, who had become governor when Ford chose Rocky to be vice-president). However, Carey's first wife, Helen Owen, had died in 1974; Carey later said that her death was the reason he decided not to seek the Democratic presidential nomination in 1976.
If Carey had sought the nomination in 1976, he would have been the only major liberal candidate from the Northeast, and AFAIK the only Catholic to be a serious contender (unless you count Jerry Brown, who only entered the race very late in the primary season). If Carey had at an early stage managed to establish himself as *the* liberal alternative to Carter, he might have had a chance at the nomination. In the general election, he would no doubt do worse than Carter in the South, but might be able to make up for it in the North. (He certainly might have carried New Jersey and Connecticut, both of which Carter lost to Ford, but that would probably not be enough to make up for his losses in the South. The big question si whether he could have carried Illinois and Califronia, both of which Carter narrowly lost to Ford n OTL.)