Assuming you didn't need a permit to buy that gun, so it shoots at under 500fps. With low velocities, you probably want to get the heaviest pellet possible. I believe you can get .177's over 8g. At that velocity, a pointed or hollow point pellet really isn't going to make a difference, a domed pellet will probably actually have more knock down power.
Even then I'm not sure how lethal a .177 at sub 500fps will be on larger blacks or greys...it will definitely have to be a head shot. As a kid, I once shot a rabbit with a .177 Crosman air rifle..didn't kill it but it was stunned enough where I could walk up to it. Fired another pellet between the eyes at point blank range, and it didn't even penetrate the skull. Ended up having to "manually" put it out of its misery.
Not sure if you're in the city, but if not, I personally find a good ol' 22LR with 38g hollow points the most effective way of dispatching pests, without getting the neighbours excited...reliably deadly and reasonably quiet.