I would think that coyotes and dogs would fall into the same catagory
This from the MiDNR website....
Note 1: Coyote may be taken on private property by a property owner or designee all year if they are doing or about to do damage on private property. A license or written permit is not needed
If a dog or coyote were about to have go-around with my dog, I would probably consider that damage.