It's not a good idea at all in my opinion. The 22 LR, even when loaded with CCI Stingers is still very under powered for coyotes. The 22 magnum is marginal at best, and considered in most circles to be very under powered it's self.
I've shot coyotes with several calibers, and in my opinion, the 22 Hornet is about as small as you can go, and still assure quick kills.