Once you reach Goldenrod City, you might find a house that has a mother. Talk to her and she might say something about Bill, her son. She will tell you where he is. Go there and he might come back home. Go back to Goldenrod and the house. You will see Bill, talk to him and leave an empty space in your party for your new eevee Bill will give you! I hope you get it.
Usually you can get what pokemon you want by having a girl pokemon/eevee and mating it with a ditto