Try and get them to explain how we distinguish God working in mysterious ways from God not doing anything at all. Try and get them either to make falsifiable predictions or notice that they can't.

If they are willing to make falsifiable predictions about things they don't know about yet, this can be a good way for them to learn that not only does God not work the way you think he ought to, he doesn't work the way they think he ought to either.

You can't topple someone's religious belief with a single argument against one of the lynchpins of their faith (it's never happened to my knowledge, at least,) but you can make them realize that this is another belief they ought to be suspicious of.

Also, if you're trying to convince your interlocutor rather than your audience, don't frame your points as arguments, frame them as points of discussion, such as "I think X because..." or "My take on this is X."