How do you get an Eevee from Backlot in Pokemon Pearl?

Well, there is a way but it may take a long time! What you do is you go into Mr. Backlot's office and save your game in front of him. Then, you talk to him. He'll ask you if you are envious. Say yes. Then he'll ask you again. Say yes again. Then he'll say a Pokemon that "a cute eyed Pokemon that joyously ran up to me." If the Pokemon he just said was not the one, turn off your DS and try again. I hope this works for you because I have caught five Eevee already in his garden! Good luck! :)