Yes coyotes are cunning and generally fearless, smart too. Yes even all that wild life is there but your chickens require less work for more gain. So there are several options you can explore. Trapping and shooting are not good ones. After 150+ years of that coyotes are more smarter and found in more places than ever before. Here are a few of my recommendations.
I am not averse to an electric line or fence. properly installed and monitored they are great. Also DC is not harmful to us or animals. But lets take that with a grain of salt, yes. Its won't kill you but depending on the amperage can really hurt. So if you have a dedicated run or area electric is the way to go. There are now electric movable fences that some people I know are using with good results.
Yes a dog is a good addition to we countrified folk. But this comes with a serious warning, your dog can be your greatest asset or your worst predator. Which way it goes falls on you. Personally I suggest a good working type dog, a herder, a guarder or a mix there off. Our dog was a random kinda mutt, only thing we knew is his father was a big black Chow/Lab or retriever mix. So he took our chickens as another weird addition to his pack. Like the cats and the kids.
The other one was a Terrier/Dalmatian mix. So both dogs where energetic vigilant outdoor dogs. You can use a herding type as a protector/controller but this requires more training. Or a guard type that is introduced to the flock at young age can be an imbedded protector. Or for that matter any large dog that won't go after your chickens but hangs around the house will work.
And those are the simplest to train, if he or she eye balls your chickens. Simply step between them, get his attention and tell him, No. Sternly no need to yell or anything after a few times he gets ah those are yours. So then he simply goes back to doing what dogs do. Guarding their home territory which happens to include your chicken yard.
The other options are, geese, lamas, alpacas, donkeys and burro's. And of course there is the ever vigilant and loud, Guinna hen or a pea fowl.