What kind of dog is it? I have two large dogs. I don't worry about coyotes b/c usually a lone coyote will avoid what appears to be a pack of larger animals.
How old are your kids? Again, if the dog is out there with the kids, that's a lot of commotion for a coyote. They're not as shy as wolves, but they aren't stupid.
The biggest issue is leaving a small dog or puppy alone in the yard. That is when a coyote will take advantage.