Coyotes can and will go after deer in the right circumstances -- usually when they live in rural areas where they can live in a pack or rout as opposed to solitary. They take deer where I live -- Ayton, ON. They certainly do take large livestock eg. sheep and calves...
The subspecies of coyote that we have here in southern ontario is relatively large, or at least, with all that fur, appears large, and often mistakenly identified as a wolf...