There is one specific to dogs: DogLayingDownIdleMarker. It's only used by Meeko, I think, but you should be able to look at his AI and Quests to see how to get other dogs to use it.
Many actors, including canines, cows, bears, and hares also have a laying-down idle that can be triggered with Debug.SendAnimationEvent(akTarget,"idleLayStart"). Goats have one called "idleGoatLieDownStart". Horses and deer don't seem to have any laydown animation, though you could ragdoll them and set them unconscious if you don't mind them looking dead rather than asleep
