What kind of bear eats a coyote?

The most likely bear to eat a coyote is a grizzly bear.

Grizzly bears are large and powerful, capable of taking down prey much bigger than coyotes. While they primarily feed on plants, berries, and fish, they are opportunistic carnivores and will eat other animals, including coyotes, if they get the chance.

Other bears, like polar bears (though they are primarily marine predators), and black bears could also eat coyotes, but it's less common.