Coyotes, yikes! We don't have a problem with them, but we do have an over abundance of hawks, eagles, and vultures (the killing kind). 300 acres of dense woodland was cleared next to our neighborhood, so the wildlife moved into the few remaining trees around our houses.
If you can, it would be a very good idea to build a small, fully enclosed doggy run made of chain link or some other metal fencing. I'm considering doing it my yard.
Stay safe!