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Is it possible to diplo-annex a country with vassals? I never seem to have any luck whenever I try this.
Yes, I've done it many times before. You can't diplo-vassalize a country with vassals, but you can diplo-annex them.
 
One more thing-

which other Christian countries can Christian countries diplo-vassalize and then diplo-annex?
Any country you can have a royal marriage with. In other words: Orthodox is compatible with all Christians, Protestant is compatible with Reformed, Catholic is compatible with CRC, and after the Edict of Tolerance, all Christians are compatible with each other.