Looking at OTL religions, the best candidate seems to be the Baha'i Faith. It's young for a religion (the Bab didn't officially declare its existence until 1844); but also one of the most progressive religions out there; its core tenements include equality between women and men, universal compulsory education, elimination of all forms of prejudice, and harmony between religion and science.
Probably one of the Faith's biggest strengths are its belief of Manifestations of God; that the Prophets of the major world religions that came before it (Jesus, Mohammed, Buddha, Krishna, Zoroaster, Abraham, ect.) all preached the truth of God in a sort of 'spiritual evolution'; each religion is the truth for its own time period, with the next Manifestation of God bringing an ever advanced revelation of the truth, and thus bringing the world closer to God. Converting to the Faith therefore wouldn't mean leaving Christianity or Islam behind and rejecting your friends and families as nonbelievers, but moving to the most recent revelation of truth, the Baha'i Faith.
As the Baha'i sprang up in Iran under a very oppressive regime, I doubt it could ever prosper in its homeland, but would do very well in developed regions (Europe, the Americas) jaded with the antiquated views of their old religions. Being a member of the Faith wouldn't mean denying science like evolution, but valuing it as a truth that brings them closer to God.
The Faith today has around 5 million followers, but those 5 million followers are spread over more than 200 countries and territories. Give the Baha'i Faith a POD that places more emphasis on proselytizing and it probably become very big very quickly.
I'm no expert on the Faith, so here's more info here if you want to take a closer look at its potentials for becoming a more major religion:
http://info.bahai.org/.