Self-banned from the alternate-history forum until October so I can focus on work and my personal writing projects, but here's a relatively new Roman-era timeline that looks pretty cool.
It's entitled "On Eastern Shores: A Roman Timeline." The divergence from our timeline is that the dying Emperor Trajan, instead of selecting Hadrian as his successor, instead chooses the Roman general and governor of Judea Lusius Quietus. Lusius had defeated a series of Jewish uprisings known as the Kitos War, which is part of reason the timeline's author gave for Trajan deciding Quietus would be his successor instead. The other reason is that Trajan doesn't think Hadrian will retain his conquests, something that our history bore out with the abandonment of Mesopotamia.
(Quietus was relieved of command and killed, possibly on Hadrian's orders, soon after Hadrian became emperor, so it's possible he was a serious contender for power.)
As emperor, Quietus finishes the war with the Parthians with a treaty that leaves Mesopotamia in Roman hands and the kingdom of Characene (modern southern Iraq and Kuwait) a Roman client. Hadrian, seeking to avoid offending Quietus, moves to Characene and becomes a patron of scholarship, including Indian and Chinese scholars whose ideas become popular.
And that's the kicker there. With a Roman port on the Persian Gulf, Rome is in a much better position to participate in the Indian Ocean trade. The Romans also receive a Chinese ambassador, something that I don't believe happened in real history. As a result, Buddhism spreads more readily in the Roman sphere than it did historically, while Confucian ideas about government arrive. These encourage the Roman Empire to develop a more merit-oriented bureaucratic system rather than staffing the government with members of the senatorial and equestrian classes.
I don't agree with everything the author plans for this timeline--he seems to think Buddhism would syncretize with and replace Christianity because Buddhism, unlike Christianity, does not require people to abandon their earlier religious beliefs. I'd prefer he go with a more religiously-divided Roman sphere (one of the commenters suggested one half be Christian, one half be Buddhist, and Christians enjoy more success outside of the Empire), but I'm not going to be a major contributor to the timeline. So we'll just have to see how it goes.