I've never killed any coyotes with a bow( or gun for that matter, too much like shooting a dog), but I've got no problems killing gophers with my bow( thanks Ron for the head's up)
I was an avid bow-hunter for ten years and was rewarded yearly with game. I find most people new to shooting a bow make the mistake of buying too much fancy gear and getting their hopes up only to be disapointed . My advice to you would be to do some research online or spend some time on Alberta Outdoorsman.com. It's also a good idea to go to a shop that has shooting lanes and take lessons. I made leaps and bounds in accuracy and technique by having an instructor tutor and correct my bad habits.
I've got a few entry-level bow hunting books that I'll dig up if you want them.