A coyote smiles when it is happy! I have noticed coyotes smile especially during and after playtime.
Smiling is also a method of purposefully communicating goodwill. In this sense, I’ve seen smiling during play, when “getting rough” might have overtones of aggression which could easily be misinterpreted. Since playing incorporates all the moves of real-life fighting — even though it is “not for real” — play could be interpreted as aggressive if it were not for the smile. I have also seen smiles used as a communication device to disarm another coyote who is angry. Smiling signals “I’m not a threat to you. I’m not going to challenge you. I want to please you. I like you.”
And, I have had a coyote seemingly smile at me: “Hey, I see you down there and I’m okay with that.” Facial expressions function the same way in coyote society as it does in human society. Coyote society is highly socially organized according to dominance and pack loyalty, so it comes in handy.
Related to this is showing the tip of the tongue. I see this as a small kiss. It appears to communicate the same message as smiling, but in this case, it is almost always when there might have been room for negative misinterpretation of the coyote’s intentions. It appears to be almost as a gesture of apology.