Your goal is get either dynasties to convert their country to Christianity as a a majority religion.
Edit: Or around those times by other forces that affect China
Edit: Or around those times by other forces that affect China
Not really technically Qing, but what about a successful Taiping Rebellion?
I believe that the best bet is Matteo Ricci, a Jesuit priest who attempted to create a fusion of Christianity with traditional Chinese beliefs. He approached introducing Christianity as an extension of Confucian teachings and ancestor worship rather than as a new religion. If the achieves more success I feel that the centralized nature and hierarchical nature of an organized church would appeal heavily to Chinese authorities. And by respecting and embracing traditional teachings he doesn't alienate the Chinese establishment as much as regular conversion attempts did.