I'd say a .22LR is marginal at best for coyote, depending on the size of the animal. Definitely not ideal, and it is a lot harder to hunt ethically if you're walking around with a gun that is always at risk of being undersized. We don't have wolves here, but my understanding is that they are larger than coyotes.
If the rifle is a good deal, however, you may want to buy it anyway. A good .22 is nice to have. They're really cheap to practice with, and great for smaller game like squirrels and rabbits.
If you already hunt medium game (whitetail deer), the rifle you're using for that is also a good choice for coyote.