I trapped a couple nuisance beavers two years ago and sautéed the back straps with onions and bell peppers. I brought it over to my grandpa's for our weekly card night. It was very good. At 90, Grandpa is slowing down a bit, so he had finished his plate before he put it together that he'd just eaten beaver. The look on his face was priceless!!
Have eaten coon many times; baked, or boil until coming off the bone, chop up the meat into a hash, add onions, garlic, a little oil, some hot sauce (preferably Texas Pete) and then lightly fry it in a skillet. Possum is best caught live and caged, fed on sweet potatoes and cornbread for a couple of weeks to clean it out and then baked like a suckling pig; always served with sweet potato or with some Cackalacky sauce over it (made from sweet potato).
About the only weird one that I have eaten is muskrat. We just battered and fried it. It was really quite good, but I could not get past the fact that I was eating a rat. It would sure beat starving, though.
My boy scout troop would host a "Wilderness Dinner" where the proceeds were used for feeding the hungry. The Dinner was in September each year which worked great for locals to empty out the prior season's leftover game.
We always had BBQ beef brisket and roast turkey but most years had most of these:
Each mother of a scout had to cook up one of the "exotics" and one year mine cooked the raccoon. Cut up like a squirrel with each leg and then the back in 4 segments. Cut up two big boars. We ran a trap line so would freeze up a couple but sold the rest to locals. Mom used a Dutch over with some water, onions, carrots, celery, salt and pepper. Most likely would get the same results with a crock pot.
Most folks filling their plates at the wildlife dinner would take a small bit of several of the more exotic items and they really seemed to enjoy the idea of being able to tell friends they has just eaten squirrel or possum, etc.
Beavers are great tasting and if you trap the meat adds up fast 500-1000# a year just by throwing a few traps out while runnning a muskrat line.
You don't really need any special recipes crock pot roast, smoked, jerked I've never not liked it.
I had possum once. The guy cooked it real slow, and it was pretty good. The other one that I thought was weird was mountain lion. It was pretty bland and tasteless. I had a hard time getting past the fact that I was eating CAT!! It wasn't bad though.