Cleetus,

With that many coyotes, I think I'd carry a rifle for the sole purpose of thinning those guys out. There is one on the land that I hunt, but the landowner doesn't want me to shoot him because he keeps the rabbit population down (and cleans up my field dressings). But he has said if there is more than one, shoot all but one. I have seen one several times while out hunting.
Here in Iowa we have continuous open season on coyote, but in Indiana you are restricted to 10/15-3/15.