The way to get an Eevee in platinum is from Bebe in Hearthome city. If really need to find one in the wild, they can only be encountered in the trophy garden on route 212 after obtaining the national pokedex. read more
Eevee will appear for two days (the day Mr. Backlot announces it and the day after), so you can catch a wild Eevee. Incidentally, if the Eevee you got from Bebe is male, and it's too late to reset, you can also try for Ditto in Mr. Backlot's Trophy Garden once you have the National Dex. read more
Eevee is a very special type of pokemon and you are going to need several if you want to completely fill your pokedex. You may want to save and keep restarting to try and get a female if you don't have a ditto. This is the first way. Remember to save your game before you talk to the girl, so you can restart. You want to get a female eevee. read more