I currently have a RAR-P in 204 that is very accurate with both 32 and 40 grain AMax.

I haven't seen a FMJ .204" component bullet that would be more fur friendly than the AMax that I've been shooting. Small animals hit with a fragile .204" bullet tend to disintegrate, while 'cats and foxes often end up with such large wounds that whatever internal organs are left inside the body can be shaken out through the wounds. Coyotes are bigger/tougher, but fist size wounds are the norm, all with major damage to the hide.