I have to agree about the Kanishka POD being the easiest. You have to start fairly early or else you have to come up with another missionary universal religion to displace the Buddhism that's already there. Judaism is a very popular cult on this forum, but it just doesn't have the size and it's a traditional ethnoreligion with only a series of very unlikely events that led to Axum converting. Zoroastrianism is out because it was the religion of the "enemy" in Parthia and the Empire persecuted it. Manichaeism would be a good candidate for a replacer of Buddhism in the Constantinopolis era, if you keep the Huns from converting to it before conquering Persia or even have them conquer Roman land instead. The Huns heading to Europe is a pretty popular POD, so I bet there's even a TL on this site already where the Huns destroy the Roman Empire and set up a Manichaen Hunnish Empire instead. Or use some kind of early alt-Dhammus Primus movement based in pagan or even Judaic beliefs. The lure of an anti-idolatry, slave-freeing, all-equal brotherhood of man is powerful and I don't think that the movement needed to be justified by the Canon in particular, just a popular sentiment. And I doubt that any Roman society around 800-900 PD(Post-Dhammus for you heathens out there.) will be lacking in people who are agitated by Roman slavery and inequality.
OOC: Manichaeism is just the syncretic Zoroastrian-Judaic-Buddhist Persian faith that took over in many cities as a new alternative to the old religions and Buddhism at around the same time as real Manichaeism. It was adopted by the Huns to justify conquering Persia, as the old regime held to the increasingly unpopular Zoroastrianism. I'm not implying Mani as we know him happened.
Dhammus is the Romanization of Dhamma or Dharma. The Dhammus Primus movement is a radical sect of Buddhism originating in Germania Inferior and was adopted by the Franks, who used it to justify their conquest of Gaul and Italy, triggering what is popularly known as the fall for the Roman Empire, even though the Frankish king Birinus styled himself as Western Roman Emperor and was recognized as such by the Eastern Emperor. Birinus' sons however soon split the Empire into the kingdoms of Upper Francia, Lower Francia, and Italy. Dhammus Primus rejects the newer teachings of the monastics and so-called Bodhisattvas of the Empire, referring back to the Pali Canon brought from India several centuries ago. They freed slaves and executed authorities they deemed corrupt but tried to maintain the local power structures and just co-opt them. Think alt-Islam, but less based on a single personality and more Roman. It maintained a unified Sangha(church) for only three generations after Birinus, where it split into a Sangha for each kingdom. The Orthodox Sangha is still united under the Patriarch of Constantinople and includes North Africa and Syria.
Post-Dhammus dating system dates from the First Buddhist Council in 483 BC. It is used mainly by the Primus Western Europe and in the New World, which was discovered by Anglian Primus explorers. Eastern Europe and North Africa use the Roman date system of Ab Urbe Condita. All European-descended cultures use the Roman calendar, much like OTL.