Question

What kind of sleeping move can I teach My Espeon?

Answer 1

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.

Comments

Ok, but how do I teach it yawn? A tm? Also what about Grass Whistle, Sweet Kiss ?

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You use breeding.  Breed a male Wooper/quagsire, Dunsparce, Slacoth/Vigoroth/Slaking, Pansear/Simisear, Bidoof/Bibarel, Hippopotas/Hoppodwen, or Munna/Mushanara who knows yawn (these are compatible pokemon who learn it through leveling up.  Smeargle is also a candidate) with a female Eevee and the baby Eevee will know it.  Eevee/Espeon cannot learn grass whistle nor sweet kiss.  Also, sweet kiss doesn't induces sleep, it causes confusion.