well.. I think that given the options you have, the terrain is going to dictate..
I would personally use a #2 steel shot, so no matter where you are you are legal, if you are hunting in Brushy area's. I would get the Carlson Dead Coyote choke (it's more than full choke)
If you have area's that are pasture and more open, then i would opt for the 17. There is more than one 17 out there and some of the newer 17's have amazing balistics (compared to the 22lr)
I would then get one of those larger ones like the A17 that is out, and use that. I would think that it is about as fur friendly as it gets and should still drop a coyote out across a pasture.
Those two options in the truck and a stool, should be a good solution. IMO