First you must get your national pokedex by spotting every pokemon in the Sinnoh region. Afterwards head to Pro.Rowan and the rest will be simple from there.

After getting your national pokedex, head to the pokemon mansion. Instead of going in the trophy garden, talk to the owner of the the trophy garden. He will ask you two questions and you must answer yes to both questions. Every morning when you talk to him he will ask you the same two questions, and after you answer his questions, he will tell you what pokemon he saw in his garden that morning. Some of the pokemon are: marill, meowth, cleffairy, and eevee.

Keep going to him everyday until he say that he saw some Eevees in his garden this morning. When he does, then you go in the garden and you will find your eevee. It may take you a minute to find the first one but you will be able to catch a few.

Submitted by Lavardo B (hotpotato78)