I always find this topic intriguing. I have a lot of coyotes on my place. Grew up in this area and we have always had a lot of coyotes as well as wild dogs. Hear several groups yelping every night. They come up to my garden and eat my watermelons almost nightly this time of year. Last spring just as it was getting dark I was doing some dozer work and had a group of seven come up and walk on each side of me heading for the watering tank - coyotes, not wild dogs. Most any morning you can see one crossing the pastures. Most of the time it is just one, some times two, and ever so often three together. I'm not smart enough to know if they hunt alone or in groups - but when I hear them in the late evenings there is certainly more than one in the group. Maybe no one told our coyotes they were suppose to hunt alone, I don't know.
But there is one thing I do know; neither I nor any person I have known in the area over the last 40+ years has ever "personnally" witnessed a coyote kill a healthy calf. I've heard people say, "Well, ol' so-and-so had a calf killed by a coyote", but when I personally speak with ol' so-and-so it is the same with most which have seen them feed on a dead/dying cow/calf but never actually seen one run down a calf and kill it. And most of the time the buzzards are there before any coyote shows up. I'm not saying it hasn't happened, I'm just saying that I have never met a person that has actually witnessed it.
There are some folks in the area that shoot them. Some because their fathers did, some that have moved out to the area on small acreage that don't even have livestock or maybe just a horse or two. As for me, I let them be. However, if I ever do actually see one run down and kill one of my calves, I will have no problem with terminating them.