lorax

Trapping is a reasonably good way to get rid of them without killing them. Look for Havahart type traps, then toss them in your trunk and let them out in your nearest national park.

I wouldn't poison possums, though - they form an important part of the diet of your area's larger carnivores (domestic dogs and cats included) and I hate to think of somebody's pet, or even a wild coyote, dying because it ate a toxic possum.