Trapping possums and coons is the best idea, especially in a live trap. Here is how I do it.
Find a good trap that will hold the animal. Make sure it is sturdy, coons and possums are tough and are known to be able to muscle their way out of faulty traps.
Buy a cheap can of tuna. Not the fancy junk in olive oil, tuna in water will do just fine.
Empty the tuna can into another container and freeze all but one piece. Take the empty tuna can and wire it to the bottom of the live trap. This is very important: possums, Coons, and you common feral cat all will try to just stick an arm in and slide the bait to the side of the trap and eat it. If they can avoid getting into the trap they will.
Take the piece of tuna you didn't freeze and put it into the trap. Tuna stinks really good and they won't be able to resist it. Make sure you set the trap on it's lightest setting. If it only has one setting make it as easy to trip as possible.
Next go Watch TV until you fall asleep or something. When you wake up in the middle of the night you should be able to hear if anything is in the trap. It will be making all kinds of noise trying to get out.
When you do catch one it's up to you what you do with it. From experience I just want to warn you if you catch a cat in that trap just shoot it. If you decide to let it free there is a good chance if will claw it's way all the way up to your pretty face. A .22CB works very well for the job, even for possums and coons. Put one in the ear or between the eyes. CB's are very quiet, just what you were looking for.
Using this method my Father and I have caught over 50 Feral Cats, several possums and coons.
Hope this helps someone.