Actually, on the top floor of the Celadon Condominiums building, which is on the same street as Celadon Department Store and the Pokemon Center and is the first building you can enter after the Pokemon Center (it houses Game Freak), there is a room where you get Eevee.
If I remember correctly, it is in a PokeBall, not given to you. If it isn't in a PokeBall, then it is given to you. :P
In order to get to this room, you must enter from the back, which you can do by moving up from the right side of the Pokemon Center, then left until you get to the Condos.
Then just give Eevee the Thunderstone.