Assist is a breeding move, and as I recall Eevee can't even learn it. If you want good cute moves and really don't give a rat's arse about it surviving in an actual battle then go with:
Charm (Needs breeding, though)/Attract
Growl
Rest
Sleep Talk
Rest and Sleep Talk make a cute appeal combo, as do Charm and Rest, and Growl helps you out if you get bumped down by appeal jamming. Attract is also a very nice move to use when your first since it has the chance of preventing others from appealing. Do remember, though, this is only if you want a pokémon that can't fight, you should also match the contest type with the pokémon's nature since it's easier to max out its contest attributes that way (Jolly, Timid, Naive, or Hasty for Cute, Adamant, Naughty, Lonely, or Brave for Cool, Impish, Relaxed, Bold, or Lax for tough, Calm, Careful, Sassy, or Gentle for Smart, and Modest, Rash, Quiet, or Mild for Beauty) the ones with netural natures aren't really worth it (Unless you're really pedantic) since it's practically impossible to max out any of their attributes.