If your dead set on shooting them, I'm with Grey Beard. I'd be using CCI short hollow points. They can be fired even through a semi auto in single shot mode.
I've been ridding barns, and such of coons, and other critters for years. My weapon of choice for indoor coon removal in a baited #220 Conibear trap. This is a slightly dangerous trap in that it'll do serious damage or break your wrist/fingers if you manage to catch your self in it(don't ask! LOL!). In most cases it's as easy as baiting the trigger with a piece of apple. If they don't go for that, then make a pouch with window screen, and fill it with sardines, then wire it to the trigger. You can buy these for less than $20 in most cases. I'd stick with the "Victor" name brand as they're a lot better made, and easier to use in my opinion.
If you go the Conibear route, be extremely careful where you place it. This trap will kill cats, and even smaller dogs stone dead. They work great though!