Traps
Now that I think about it, I do have a couple of those "dropping gate" traps that I have used on squirrels and other critters. I cleared out a small colony of four young possums (about the size of a big rat) and took them to the local wild animal center this way. I don't know if this would work on a full-size possum. I do know I'd have to get a bigger trap. Dog food makes good bait.
I have yet to successfully trap a roof rat this way, though. Eventually, one of the local cat posse gets them.