According to the Indiana Department of Natural Resources, coyote hunting is legal year-round and does not require a hunting permit when a coyote is killed on a person's own property. If hunting on another person's property without written permission, then a hunting or trapping permit is required.
Indiana's DNR explains that the coyote is considered a nuisance form of wildlife that wasn't prevalent in Indiana until after the 1970s. Coyotes are found in rural as well as urban areas and are most often observed at dawn and dusk. They are considered foragers that feed on anything with nutritional value, though they typically consume small mammals.