Espeon and Umbreon are certainly one of the more involved Eevee evolutions, since they require you to actually use Eevee in battle and keep them in your party for a while. This is because the only way Eevee evolves into either form is by strengthening the friendship between them and the Trainer.
There is a quicker way to get both Umbreon and Espeon that will still require you to use them in your party, but have your friendship grow at a quicker rate.
First make sure to catch two Eevees in Luxury Balls. You're given five of them through the main story quest. Alternatively, after you get access to the entirety of Lumiose city, go to Autumnal Avenue and there is a shop with a Pokeball sign. This shop sells all the special Pokeballs, including Luxury Balls, for 1,000 each.
The reason you want them to be in Luxury Balls is because their friendship level rises much quicker than in any other Pokeball.
After you successfully catch your Eevee (or two) in Luxury Balls, make sure to give it a Soothe Bell. This item further increases the level of friendship gained by having Eevee in your party, leveling it up and winning battles with it.
All it takes then is to go out and win a few battles. Eevee doesn't necessarily have to be involved, since EXP share will allow it to level as well, but you do get friendship easier if you actually use and win with Eevee. It took us around 10-12 levels for Eevee to gain full friendship and evolve.
Remember, to get Umbreon, you have to level Eevee up after 8PM and before 4AM. Alternatively, Espeon is attained by leveling up Eevee after 4AM and before 8PM. Basically one needs to level up at night, while the other during the day.
