Catholic Japan could have been a possibility. A better run Otomo could have managed it with the right benefits and bonuses. Protestant one is notably more difficult and would require a leadership that wasn't so protectionist and isolationist I would think, and they still would not have much of a chance IMO. Oriental Christianity such as Nestorianism could have managed it if they became stronger rooted in China and Korea, but still not as likely as Catholicism.
In short, it's doable to make Japan Catholic, require some dice loading for Nestorianism, and is damn near impossible for Protestantism.
Hmm, what if the Tokugawa Shogunate was never established and the Toyotomi remained in power?
Protestantism could happen if they were converted to Christianity by Catholic priests, and by Christianity I mean the basic Idea of Christianity where for the most part they could see little difference between Christians in England and Christians in Spain.
Maybe 200 years down the line with English and upcoming American influences they could be slightly leaning away from Catholicism.