As others have mentioned, strangling Islam in the cradle nets you at least the Levant and North Africa, and could get you Persia as well. This probably also leads to the Christianization of parts of Central Asia going on into the future, although how effective that ultimately is is dependent on what sort of competitor (if any) is coming out of Persia.
China is a tougher nut to crack, and I don't think the Taiping suggestion will really cut it--I'm skeptical that the Taiping would manage to Christianize China completely in the long term, and if they did their beliefs would be so syncretic that it'd be hard to call them "Christian" in any real sense. I think an earlier POD might be better there.
During the Tang Dynasty there was a very notable period of, for lack of a better term, spiritual yearning in China, where people began to take interest in more spiritualist/mystical religions over traditional Chinese religion, which is very formalistic and not very "faithful" in the sense of not really emphasizing salvation and so forth like, say, Buddhism or the Abrahamic religions. It's during this period that Buddhism expanded considerably and Islam arrived in China--the former became very widespread after a few centuries, and the latter at least succeeded in carving out a small but devoted population inside China. You could probably have Christianity arrive more heavily during this period as well--it did in real life, but it never really caught on. If the lack of Islam leads to a Christianization of Central Asia by some sect or another, that Christian sect would be well-placed to expand into China.
Two things could then allow it to expand further. You could have the Great Anti-Buddhist Persecution overlook the Christians or hit the Buddhists much harder than the Christians, allowing Christianity to take over the gap left by Buddhism as a more mystical and evangelistic alternative to current beliefs, and then you could kill of Zhu Xi, preventing the creation of the Neoconfucianist school that would arise to counter the ascent of these evangelical religions with a more spiritual set of beliefs that are in line with Confucian orthodoxy. While this isn't going to get you a China that's majority Christian, it could give you one where Christianity is a significant portion of the population, and well-placed to convert most of China over the next many centuries