From what I've heard the best case scenario for Carter is some situation in which the Iran Hostage Crisis happens, but ends at just the right moment for him, and then the debates are somehow avoided. That is, perhaps I have my facts wrong, but I seem to recall that the crisis, at least initially, helped Carter. That is, the rally around the flag effect it engendered initially favored the incumbent. The crisis helped Carter avoid losing renomination to Edward Kennedy. However, as the crisis wore on, it accentuated the sense that he was a politically impotent figure, and helped Reagan defeat him in the general. So you might need there to be a crisis that lasts long enough for there to be an incumbent boosting rally around the flag effect, but not long enough for Carter to look woefully incompetent and impotent. Unfortunately for Carter's chances, I have no idea how to pull off that scenario. Avoiding the debates is easy enough, as I recall reading/hearing, they were only barely agreed to historically. If I have the record straight, Reagan wanted Andersen on the stage, Carter did not. So it's easy enough to imagine a situation in which the two don't reach any agreement.
Given these two conditions, I think it's at least slightly within the realm of possibility that Carter pulls off a narrow victory.