1992 was, according to early commentators and an old SNL sketch, Bush's race to lose. Following '84 and '88, people (especially apathetic Democrats) expected another loss with presumably '96 being the big chance against Quayle or an open seat.
History, obviously, followed a different course, but if for some reason the economy was better, Bush had less trouble with foreign entanglements, or some national tragedy propelled him into popularity amongst even the Republicans if not the nation, then it'd be *really* seen as an unwinnable situation, and maybe you could get the big names (Brown, Clinton, Tsongas) to drop out and wait for next time. Not sure why Jimmy Carter would get involved at all in the race. He endorsed Clinton on April 1st, but I'm not sure what else he was doing that year.
The only way he could run is if apathy was so high and the DNC was sure they would lose. But even then, I imagine there are better candidates willing to jump at a chance to serve as a sacrificial lamb. Once he gets the nomination though, any number of things could suddenly blow Bush out of the water (including the dreaded HRP torpedo), but '92 is still pretty close to the Carter years in memory that the electorate will be driven way, way down and you won't get many MTV voters, making the race a toss-up at best.
A non-consecutive Carter who becomes President would leave the 1996 race wide open. It could very well be Dole v. Clinton, or maybe Carter's recent example would provide motive for Bush or even Ford to try again.
He might be busy enough with Habitat for Humanity work at that point.