put up three motion detectors in a triangle to cover about 15 yards. Coyote CAN NOT SEE THE COLOR RED, so put red lights in the sockets. They step into the triangle to a feed pile, lights come on. Now, on another motion sensor, have an alarm go off by your easy chair and/bed. Install a fake door in your back door, piece of plywood/plastic cardboard painted flat black. Have a shooting table with your 22 RF ready to go, with hole in the fake door for you to see through with scope. Have your gun set up where your cross hair is on the dog food. Don't shoot immediately, try and determine just how many they are. The one with his head stuck in the feed bowl is not apt to run off(Dominant animal), shoot another one first. Don't shoot at eyes, as they maybe your neighbors pet.
Use a flash light with a red lens filter to see your way though your house when the sensor goes off while you are sleeping. Mini mag light makes these. If you need light to reload with, leave your mini mag light on at the shooting bench, this will also help if you have a jam or fail to feed, the light will already be on. Caution, even a 5 watt night light near your shooting bench will sabotage your success.
Remember the color spectrum:
Red
Orange
Yellow
Green
Blue
Indigo
Violet
Nocturnal animals can not see red, they can see orange, yellow more, and can definitely see Green.
Use sub sonic 22's, shoot the coyotes in the lungs so they will run off, more will come. Be sure your muzzle is inside the house(further the better), not outside the fake door.
Take 4 cans of sardines in oil and pour them down a tree or post at your feed pile to add as an attractant, they can smell it for half a mile down wind or more. Put an orange sticker on the post and shoot your sub sonic 22's into that target as a reference for that distance.
Best time to bait like this is when a low pressure front is approaching or is over you.
Also, feed them for a while before you start, they meander in and out all night. Your wife may make you set up your "alert" in the spare bedroom because she will get tired of being woke up.
RWS sub sonic HP work well for this kind of work.
When you shoot one and he runs off, if you have done your job properly in not turning on lights in the house, getting set up quietly, you should get more than one. Don't run through the house, to the coyotes this will sound like an elephant is charging. Also, you may want to move some furniture around, so you do not run into it in the dim lit conditions(I broke a toe).
If you use a Ruger 10/22, be sure that your empty will not make any nose on what ever it hits, this cost me a couple of coyotes. You have plenty of time, manipulate the bolt on your action, quietly.
Combine sardines on the scent post and dry dog food with a can of wet cat food(leave the can), and you have a coyote meal that is simply beyond their ability to resist.
You have to observe all hunting regulations, baiting maybe illegal in your state, and don't shoot your neighbor's dog.
Experienced coyote hunters that have years of experience all have one thing in common, they use the color RED when using a light that casts a beam.