Oh, but they did!

It's called the Taiping Rebellion. It was roughly 15 years long, near the end of the Qing dynasty. In fact, it's one of the deadliest wars in history, with estimated minimum of 20 million people dead, and likely much more.

I understand that the rules frown upon simply throwing a Wikipedia link at the question, but the article is reasonably well written. http://en.wikipedia.org/wiki/Taiping_Rebellion

If anyone else could toss in further details, I would appreciate it, as I am on a bit of a tight schedule.

China did have a Christianity-fueled rebellion. The Taiping Rebellion was led by a Chinese man who claimed he was the brother of Jesus, and who attempted to impose a theocracy based on his interpretation of Christianity.

In addition to the Taiping Rebellion which has already been mentioned by a couple commenters, there was also the Boxer Rebellion which was in large part a Chinese response to the power given to Christian missionaries in the country. It was generally an uprising against foreign influence, but one of the ways this was most strongly manifested was the murder of Chinese Christians by the Boxers as well as the targeting of missionaries in particular, being a much more visible sort of foreign presence.

The Boxer Rebellion directly led to the invasion by the Eight-Nation Alliance which in turn contributed greatly to the fall of the Qing government.

Korea reacted harshly against Christianity during the same time period. At first, it was thought to be consistent with Neo-Confucianism by intellectuals who brought Matteo Ricci's books to Korea from China, but then some Korean Christians started destroying their ancestor tablets because the rituals involved for honoring your ancestors resembled worship too much for the Catholic missionaries. Once that happened, Christianity was deemed bad and was suppressed.

Follow up question, why was the Philippines such an exception?