Sure, Focus Blast would be fantastic for all of the 'eons, but is it true to Eevee? Eevee typically has normal moves along with afew other reasonable moves for it, such as "Bite".
Eevee already learns support moves a la Baton Pass and there's little better than Adaptability + STABBED Return, and you really don't need to learn Return when it's TM is always available.
Facade would be pretty good... only Flareon would be it's theoretical best user of it, and it's fire typing means you'll have to use a Poison Orb to activate Guts instead of the Burn one.
I don't think Recycle makes much sense on an Eevee, and Slack Off would be OP, so I would recommend Fake Out. It would work great on most Eeveelutions and it true to the type of moves Eevee learns.
The topic only says "Give any Eeveelution, and Eevee" so I'll choose just one.
Umbreon: One of my favorite Eeveelutions, and the one that every generation has time and again been swept aside in favor of Vaporeon. It's easy to see why; all those fighting pokemon and Vaporeon's good Sp. Atk, HP stat, and typing makes it even better at stalling or tanking than Umbreon.
So let's see if we can fix that in two moves.
First, let's give Umbreon Haze; no more setting up on an Umbreon and Vaporeon already has every move any pokemon could want. For the second move, I really liked the idea above in giving Umbreon Extremespeed, it'll be a pseudo-Faint Attack so that kind of works and without any real reflect attack, fighting pokemon and steels aren't going to be stopped by an Umbreon without going into one of the other eeveelution's types.