You can go on the Global Trading System (GTS) and ask for an Eevee and trade them with a pokemon you are willing to trade. The only problem is you have to have wireless wifi connectivity nearby. But there is another way. Get another person who has an Eevee of the opposite gender to trade it and breed it and give your friend to of the opposite genders back so they can breed Eevees too (It's just nice to do).
There is a group system in the pokemon games. If you have pokemon of the same group they will breed. Just figure out what group eevee is in and then find a pokemon of the same group to breed with it
Put amother evee with evee in day care