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).
