When I began shooting long range it was with a cheap 3-9X40 Bushnell on a .30/06 M-17 Enfield. It wasn't long before the 12" plates were falling with boring regularity at 850 yards, so yes, I think a good 3-9X is fine for coyote hunting.
Don't get caught up in the idea that more magnification is automatically better. The purpose of magnification is to enable a shooter to see his target; so magnification must be balanced with the type of shooting you intend to do. High magnification results in problems which under some circumstances can be challenging to overcome; the field of view narrows, your shakes become magnified on the target, and the eye relief becomes far more critical. If you can see the target, you don't need more, but if you can't find a moving target in a scope set to its lowest magnification, it has too much. Often a hunter is so concerned about his ability to make a long range shot that he disregards what it takes to make the close one. When the magnification is correct, your problem is simply a marksmanship exercise. How far away can you keep your hits within say 3" your aiming point? That, rather than magnification, that will determine your maximum range on a live target.