As a rule, I much prefer to not kill coyotes. When you take out a mature animal, younger dogs move in, and there's a learning curve that everyone goes through. A mature coyote that knows what the basic rules are is much less trouble than a young dog that doesn't know any better.
Unfortunately, it's hard to teach the coyotes the rules. I lost a sheep yesterday, and I found this one this morning. This sheep shows pretty classic coyote wounds. You can click on any of these pictures for a closer look. In the top picture you'll see a wound on one side of the neck. In the picture below, a wound on the other side. You can see the canine teeth marks in the lower picture.
I don't know what happened to the mature dog that used to be on the other side of the fence; this may be an interloper, or maybe the older dog isn't with us any more. I tracked the coyote to where it's entering my pasture. This ewe was attacked 15' from my barn.
Since I've had two attacks in two days I don't feel like I have much choice. I cleaned and oiled the rifle tonight, and I'll be sitting out tomorrow morning waiting for it.