I do not hunt them my self but i know that people can get them by bow but it might be a bit more tricky the coyote is SMART and will easily spook and a crossbow might work but a coumpound is going to work to and i ohio the seasons for'em is open all year long but u live in Tennessee i do not know if it open all year round there but i would hunt them in the fall or winter when there fur becomes thicker they look better...!