Seems to be a pretty good mix in the replies. I do understand the "encroachment" posting, but tend to side with the "get rid of the problem" posts. I have a different situation, I have a semi-rural 10 acres. Shooting a coyote would not only be legal, but appreciated by my neighbors. That said, I do think it's my responsibility to build the best coop I can, addressing as many threats as possible in the construction. Sounds great and I sleep well at night, but I just can't take the freedom away from my birds. They seem to love to free range and I love the reduction of bugs and mice (I love seeing the hens break out of the barn for a quick game of mouse rugby). I never knew they caught mice, but they do and it's hilarious. I have one Barred Rock who I am certain out performs the lazy barn cats around here. - Getting off topic.
I too have lost hens to coyotes, but I guess they are gonna hunt them, I'm gonna try and stop them, but I know that and populate my flock accordingly. I have an egg target, know I can get what is needed plus a little extra with 8 hens, so I keep 10, and bring in enough new blood every year to deal with the occasional loss. I have a great perch to observe any coyote activity and use it when the howling gets close or spotting is frequent. Unfortunately gun oil must smell worse than chicken smells good to Mr. Coyote. To date keeping more hens has proven more effective than whacking the predators, that said, they understand they are persona non grata around here and most sightings are of the south end on a high speed north bound escape. Many of you are probably thinking I'm some kind of wacky hay-seed, but protection of my flock is part of the deal and I will admit can be kind of fun.
Classic American literature, man vs nature, man foolish enough to think nature is conquerable, nature defeats man, but man wins just enough to not become tragic. I look at it like Hemmingway, my wife looks at it like Elmer Fudd during rabbit season. OK - Once again, back to topic.
If you don't find these tactics against your moral fiber, go get a good pellet gun. Spend a little money, get a break open with a scope in .22 caliber. Read the manual, and if you have a knowledgeable friend, maybe they could show you the basics. This is not a guy only thing, studies have shown women tend to be very good natural shots (something about hand/eye coordination). Get some cans and go try it! I would bet you have fun plinking targets, your neighbors will never hear you and you will have more than enough to send Mr. Coyote back through the fence. If you do this, be safe. These guns are not toys, but they really can be fun too. Your chickens will be really proud.