A lot has been mentioned about the regulations. Here is the MN regs. on unprotected mammals including coyote.
UNPROTECTED ANIMALS
Residents and nonresidents are not required to have a license to hunt unprotected species including coyote. Nonresidents do not need a furbearer hunting license in addition to their small game license to hunt fox.
Unprotected Mammals:
Weasels, coyotes, gophers, porcupines, striped skunks, and all other mammals for which there are no closed seasons or other protection are unprotected animals. They may be taken in any manner, except with the aid of artificial lights or by using a motor vehicle to drive, chase, run over, or kill the animal. Poisons may be used only when the safety of humans and domestic livestock can be ensured and in accordance with all label regulations of the state Dept. of Agriculture and federal Environmental Protection.