The last possum that was unfortunate enough to cross my property during daylight hours got a nice pretty .22-sized hole through its ear and was very dead within a minute or less. I use my trusty .22 LR single-action revolver for small predators like that. Rifles are for longer range and the more experienced marksman, and shotguns are too messy and noisy. .22 plinker pistols are the way to go.

This is an old thread but still pertinent. Glad you were able to get the possum. I have had a bird in the past killed by a possum. I set a live trap and caught it and then I eliminated it. Good luck and have fun...