Max out its happiness by -
- catching the Eevee in a Luxury Ball
- getting a massage in Cyllage City (house to the left of the PKMN centre)
- juices from the juice shoppe
- give them soothe bells (you can only get one from a woman in the house west of the PKMN centre in Shalour)
To be honest, just put them in your party and do something else, like run around ev training, using friend safaris, or do all the things above and do this:
- get the Eevees
- go to Lumiose City & go to the Prism Tower
- set your bicycle to cycle around the tower (so that just pressing left or right will cause you to go in a circle); make sure you avoid all the NPCs
- put a coin under your circle pad to make your bike go around by itself
Leave your 3DS for a while like that and your bike will run by itself, meaning your Eevees will slowly gain happiness.