Nero had some dealings with Christians, who were reputed to do scandalous things, and he might therefore be interested in joining them ...
Nero might be too early. At time, as far as I know, the Bible wasn't even translated to Greek, and Saint Paul was still around preaching the new religion on Asia. Christianity was still seen be outsiders as some weird Jewish cult. It was still a long time before I gained it's appeal even in the eastern part of the Empire, and established a foothold on Egypt and Syria, for example.
I'd say an Emperor around the Crisis of the Third Century might be more feasible, even if I'm not able to point out which one. The fact Aurelian and some of his successors strived to consolidate the Imperial Cult with the religion of Sol Invictus might not be necessarily a prospect of moving to monotheism, but it demonstrated a conscious effort of associating specific religious figures with the Imperial authority, which was replicated by later Christian Emperors, well into Byzantine era.
Perhaps if one of pre-Constantinian Emperors somehow realizes how useful this allegiance between the fledgling Christian identity and the Imperial rule might be.
Anyways, its convenient to remember that IOTL there was a significant span of time between the legalization of the Christian cult and its straightforward adoption as official religion of the State.