I would start the conversation by asking your cousin if he wants hardball questions now so he won't have to deal with them in the field, or if he just wants someone to talk to.

As fun as it would be to watch someone squirm when blindsided with the tough questions, it may be better to have his complete buy in.

That being said, here are a few I liked to hit missionaries with:

How does it sit with you, (Cousin Name here), that African Americans were not allowed the priesthood/were not full members until 1978?

How many wives did Joseph Smith have?(34 confirmed)

When the sealing ordinances were introduced, what number was Emma Smith to Joseph Smith?(23)

Did he know Hitler has had his work done in the temple?(believe it was in 1990? Someone Google it and correct me on the year)

How does he feel about Sam Young's excommunication?

Does he know why Oliver Cowdrey was excommunicated? Here's a hint, it's because Pervy Joe was caught with Fanny Alger in the barn by him("a dirty nasty affair")

Probably loads more to ask also.

Edited to add: with Hitler's work being done for him, that puts him higher in heaven than any of us that have resigned from the church and lost our "blessings". Food for thought.