As to coursing, laws in most states are pretty specific as to what you can use dogs for. Birds aside, you can't use dogs to break deer, but I believe you still can some places in the south. You can use dogs for bear. I'd be surprised if they could be used for wolves, or even coyotes, anywhere.
My quick perusal of the Idaho hunting regulations suggests that you could course coyotes in Idaho. The only big game animals where dog hunting is allowed are bear and cougar. So wolves would be out. However, coyotes are explicitly exempted from the list of big game animals, so absent finding any specific prohibition, I would assume that dog hunting would be allowed on coyotes. If I were going to course coyotes in Idaho I would check with the Fish and Game Department to make sure my interpretation is correct.