Sorry for your loss do you live in a neighborhood or out aways by yourself, Urban critters are a lot different to deal with than country critters
I don't let my chickens out until after lunch each day to reduce the distance they wander. I keep a loaded .22 magnum above the front door for times when I spot a critter that needs dispatching. If I had to go unlock, load and prepare every time I needed to shoot something, I wouldn't get much accomplished.
I used to deal with coyotes as indicated above successfully but gun is no more of a problem with little kids about. Birds also had cover they could retreat to which cut but did not stop losses. Best system for me has been use of dogs out with birds. Electrified fencing can also help even though coyote can usually clear such pretty easy. The risk of getting zapped makes hunt more dicey, kind of like trying to pick berries from prickly briar patch that also has poison ivy. The electrified poultry netting works real well. Remember, it is a coyote today but another critter will be happy to do same. Make the job more difficult for all of them. For me, if I can control Mr. Fox's take I can control anybody during daylight. Most of my birds free-range during all daylight hours but a couple dozen are not confined even after dark. Roost locations also need to be considered because coyotes in my experience are a little more flexible than foxes when it comes to going after your birds.
Odds are she will treat coyote like another dog. She will attempt meet and greet, coyote will be rude and if your dog has aggressive inclinations she will attempt to show coyote who is boss. Coyotes seldom have interest in working out pecking order with larger domestic dog since it could get hurt.
