The Coyote is a Minor Villain in Home on the Range. She appears in the intro, trying to eat Lucky Jack, but he escapes her and she doesn't appear again.
She returns in a deleted scene to chase Lucky Jack and the lain cows but ultimately met her demise when she and most of her pack are lured of a cliff to fall to their death. Because this is a delted scene, it is unknown if it should be considered canon.