Here are 2 suggestions:
1. Others have suggested re-inforcing your chicken pen & house, and that's very good advice. Also put up motion sensor lights if you can. When the light comes on the coyotes will probably bug out. If they get used to the lights and don't run off, then they make easier targets.
2. Coyotes are very sneaky and wary, so getting a shot at one is pretty hard to do. Around here they are more active at night, and that's when it's hardest to see one and get a shot at it. Tape a good bright flashlight with a pusbutton ON/OFF switch along the under side of the barrel of your .22 rifle. Shim it so that it shines right where the rifle is pointing when you turn it on. The ON/OFF switch should be right near your thumb when you are holding the rifle up and aiming it. Now you have an anti-coyote weapon that is effective 24/7.
You .22 rifle is adequate for coyotes. Aim for their chest cavity (lungs and heart), right behind the shoulder thru the ribs. Don't shoot at their head. The brain is pretty small, and if you don't hit it you just inflict a nasty and painful wound on the coyote. Even tho they are terrible predators, they shouldn't be made to suffer unnecessarily. A more powerful rifle would be more effective (and more humane). The .223 is a perfect coyote caliber. A shotgun (12 ga with #4 buck shot) is also a very good home defence (and livestock protection) gun and you don't have to worry as much about what's beyond your target. A rifle bullet (even a .22) can richochet and go a long ways, possibly hitting something, or somebody, far in the distance. A shotgun's pellets don't go much beyond 200 yards.
