If you really want to get him with a bow, you certainly can, but you're going to have to create the setup to do it.
You're basically going to have to get him coming to a bait and use a blind and you're probably going to have to do it at night.
First, you'll want to identify his travel route and the time of day he uses it. I've found them to be fairly habitual unless shot at. I assume he's coming around human scent regularly, so that's a bonus for you. If you have a trail camera, set it up along his travel route. Take a small bit of dog food, douse it with bacon grease and put it in a spot in front of your camera. If you can, refresh the dog food/bacon grease every day. Don't leave a lot of it, you don't want to feed every hound in the neighborhood. It will only take a couple of nights for him to start seeking it out.
Next you'll need to create a blind. The best would be to use a pop-up type, but if you don't have one, some netting will do. You will just have to be extra conscious of your movements. You'll want to put it on the down wind side of the trail. Brush your blind in well and give yourself a clear shot to your bait spot. I'd say the ideal distance will be from 12-15 yards. If you don't have a pop up blind, make sure you use some fabric of some sort to fill in the voids in your blind. You want your silhouette to be completely blocked.
For your seat, make sure whatever you use is comfortable and silent. You don't want it to squeak when you move to shoot. The best thing to do would be to dig you a pit to stand in and use the back of the pit to sit on. Use a piece of foam to keep from freezing your butt off. If the ground is frozen, use a block of firewood. Pic a seat height that will require a minimum of moment for you.
The kicker in all of this will be that you'll probably be shooting at night. You'll need to rig up a light. You can rig up a light directly above your bait by using a battery powered blind light. They are battery powered LEDs and give out a surprising amount of light. Get the green LED ones. Coyotes can't see in that color spectrum, but you can. A luminock might be a good choice, too.
When the time comes, prep yourself first. You'll want to be as scent free as possible. If you're using a blind, you don't need to worry about camo. If using a ground blind, camo yourself up real good. Make sure you darken your face and your hands. Also make sure you're not wearing anything that will snap, crackle, pop, or squeak. Wear rubber boots and use scent killer. Make sure your bow is silent as well. No rattles.
When you get to your blind, place your bait in a little hole under your light and cover it with some dirt. Leave a couple of tidbits on top of the dirt. Don't touch anything with your bare hands.
As you settle into your blind, make sure everything you need is within easy reach. Again, you don't want any extra movement. Take some cover scent (doe urine will work) and spray it all over your blind. Make sure you get settled well before you expect the coyote to show up.
When he comes, everything will happen pretty quickly. He should stop and inspect the bait. Let him eat the top pieces. You'll want to wait to shoot while he's digging. You want to hit him through the lungs. Broadside is best. If, by chance, you miss on the first shot, don't panic. Just don't make a sound. He might dash off, but if you remain quiet, he'll come right back. If you end up missing him and spooking him, well, then you'll have to change tactics.
You'll definitely want to practice shooting at something at night. Some folks have a difficult time if they can't see their arrow.
Good luck, and let us know how it turns out.