Chickens panic and this more times than not causes them to be easy prey..
Now if they can fly over the fence. 4' fence? 5, 6 ? Then they most likely got out and eaten. Don't be surprised there are no feathers. Feathers blow away and it's not likely a coyote needed to do more than clamp down on a chicken to kill it.
One only needs to watch a nature program to see what a bird of prey can do and most likely would have left some sign of an attack.
If you've seen coyote before it's most likely them. I had a dog next door that would scare the chickens to one end of the yard. As I stated chickens panic and most likely went crazy at the sight of coyotes and especially with them running up and down along the fence like dogs/coyote do.
Are there no neighbors near by? Is the area an open space? How big of an area are we talking about? Do you have pics of your yard?
I've seen hens and roosters both run and stick their head in a corner like and Ostrich. Easy pickings for anyone or anything.
I suggest three things.
One, a covered run attached to the coop so they can go out when your not home. ( I let the girls out in the yard when I'm home and the weather is nice.
Two, that your husband (this is a males only thing) go out when it's safe (no one around) and "mark" his territory. Laugh if you must but I've been doing this for two years as many times as I'm out there and need to relieve my self. So far no preds in sight. I even walk into the woods and mark the trees. And for heavens sake use a flash light at night and only when he's sober. It won't be pretty to fall in the prickers.
Three, traps or a gun to deal with the coyotes.
I wish you the best,
Rancher