I have been to bebe and Got an eevee but I want another one. I kind of ruined my chance with the mansion so I wondered if there was another option besides trading.
(I have the game pearl)
You have a 5% chance of getting one from the Backlot in the Trophy Gardens.
In D/P/Pl, it won't realize time changes and will allow you to set the clock to 23:59 and go to Mr. Backlot, redoing the process until you get Eevee as the special trophy Pokemon.
you could breed some in Solaceon Town. if the one you have is male you will need to get a ditto though.
Breeding him/her with Ditto will be your best option.