This is the only site that you can depend on for pokemon answers,and I want to get Eevee's evolved forms in Pokemon Black Version.I've been searching and I'm hoping that this site will stay the way it is.
Well, you'll need to evolve them from an Eevee, and unfortunately, you can't get an Eevee in Black. If you do get an Eevee, though, here's where you can get the Eeveelutions.
Leafeon: Level up Eevee near Moss Rock in Pinwheel Forest.
Glacion: Level up Eevee near Icy Rock in Twist Mountain
Umbreon: Level up Eevee while full happiness at nighttime.
Espeon: Level up Eevee while full happiness at daytime.
Vaporeon: Use water stone on Eevee
Flareon: Use fire stone on Eevee
Jolteon: Use thunder stone on Eevee
Hope This Helped :D
You will need to transfer Eevee in from an older game, or trade via GTS. Some of the pokemon are used by trainers after defeating the elite four.
Vaporeon/Jolteon/Flareon: Use the Waterstone/Thunderstone/Firestone respectivly. These can be found in dust clouds in caves.
Espeon: Level up with maximum happiness during the day.
Umbreon: Level up with maximum happiness during the night.
Glaceon: Level up on the bottom floors of Twist Mountain
Leafeon: Level up inside Pinwheel Forest.