Do coyotes like to eat small rodents?

Yes they do. In many places, small rodents and young rabbits make up most of their diet. If well fed and otherwise fit and healthy, it is often observed that coyotes appear to enjoy hunting the smaller rodents, making a game out of it and playing with the prey in a manner similar to the way that cats play with mice they have caught. read more

Coyotes are omnivores that mainly eat small mammals, including rabbits, squirrels and mice. They adapt well to the food that is available in a particular region, which is one reason they survive well in diverse places, including suburban areas. read more

Sorry to disagree with the other two answers here, but from my experience coyotes are capable of a lot more than just small dogs. Pound for pound, a typical coyote could take a typical domesticated dog. More importantly, coyotes will sometimes travel together to take on enemies. My father's hunting dogs got torn up on more than one occasion from that. read more