After googling a little bit, I was disappointed by nothing but religious rhetoric, so I checked out reddit.com/r/historicalwhatif, which gave me a couple of ideas. One was that Jesus wasn't necessary for Christianity, and that some other Messianic leader would have filled that role. A good theory for those of us who reject the "Great Man" idea of history. But the very existence of Great People in the game seems to indicate Sid Meier's thoughts on that matter.
That being said, another interesting idea I encountered was that of Mithraism instead becoming the dominant religion of the Roman Empire. In an article entitled "Archaeological Indications on the Origins of Roman Mithraism," Lewis M. Hopfe writes that "Today more than four hundred locations of Mithraic worship have been identified in every area of the Roman Empire. Mithraea have been found as far west as England and as far east as Dura Europas. Between the second and fourth centuries C.E. Mithraism may have vied with Christianity for domination of the Roman world."
To model that in the game, sparing Jesus means you found Mithraism, killing him means you found Christianity. For the sake of simplicity, we could imagine that Eastern Orthodox Mithraism and Protestant Mithraism split off at later points in the future, so instead of having a religion screen cluttered with three new religions, we could just have the three slots for Christianity say "Roman Religion," "Orthodoxy," and "Protestantism," and when the Roman player makes their decision, "Roman Religion," will be changed to either "Mithraism," or "Christianity." The one difference would be that "Christianity" would be renamed to "Catholicism" after the Great Schism, whereas Mithraism's name would stay the same.
As far as effects of your decision go, perhaps founding Christianity could negatively affect the stability of your empire (giving the Roman player an incentive to reenact history by persecuting Christians), until you convert to Christianity, at which point it would strengthen the stability of your empire to a greater degree than it was negatively affected by the interlude between founding and conversion, a la Constantine.
Perhaps founding Mithraism could give you a cultural bonus, which would not only model a more unbroken chain of continuity of Roman religious thought, but also have the side effect of increasing the defense bonus of your cities, useful for fending off barbarian incursions. This way, both choices are attractive, and the player could select the decision which complements his/her playing style the most.
Edit: Perhaps we can make Mithraism scripted to be founded in Rome, and Christianity scripted to be founded in Jerusalem. This way, the Roman player would be incentivized to capture Jerusalem, as Christianity would be autofounded in a non-Roman Jerusalem, depriving the Romans of the opportunity to found either religion. This would also resolve the odd situation of Christianity being founded in the Medieval Age.
In vanilla Civ IV, the opportunity to found a religion was a nice incentive to tech faster than other players, but in a mod such as this which strives for historical accuracy, I think we could stand to make Christianity (or Mithraism, if Rome controls Jerusalem and spares Jesus) autofound in the 0-50 AD range. After all the game already autofounds Buddhism, and it may as well auto-found Islam and Confucianism/Daoism. While I'm on the subject, I was playing a game as the Persians last night, and I had to restart three times until Zoroastrianism was founded in Parsa. Perhaps Zoroastrianism should also be autofounded.