Thanks for the tips so far guys.
As I mentioned before, any lethal or injurious methods are out of the question, as are things that ATTRACT cats, like sardines, meat, grease etc.
The only bait I can find that the cats don't want anything to do with is marshmallows, which is okay because the coons love them and keep coming back for more.
I've wired one end of the trap closed, and wired a marshmallow as far back in the closed end as it will go, hoping that would make the coon have to enter far enough to trap him. I even put a brick on the falling door to close it harder and push his ass inside, and a full salt block on top of the trap to anchor it down.
3 of them flipped the trap over and picked the marshmallow out from the underside of the trap, all the while smiling and mugging for my trail cam.
I'm going to stake the trap down with 18" rebar hooks into the ground tonight and see if that helps.
If it doesn't work, then I'll be looking into one of those traps mentioned above.