Well for something like a rabbit, most terriers are up for that. Same goes for rats. Possom i dont know anything about. Fox above ground (so long as they can corner it or they wont catch it) again any terrier. Fox below ground, patterdales are the hardest. Lakelands and jacks are good too. A bloke round here who is the local terrier man and does all the earths for the keepers uses lakeland x jacks but owns a patterdale too. As for coyotes, i dont have any experience of those but i know there big c**ts and are a handfull. Considering all that i would go for a pack of patterdales.