Yawn is the only move Espeon has that can induce sleep. However, it makes the pokemon drowsy the turn you use it, then puts them to sleep the next turn, meaning it won't work right away. Yawn is used more for forcing switches since your opponent will probably have to do so regardless if they try to switch or not.
It's Magic Bounce ability could be useful for this, albeit more situational. You could come in on a spore smeargle or something like that and put the opponent to sleep that way.