I recommend giving the Eevee a Soothe Bell, too. Also, when I am trying to evolve Pokémon by happiness, I rarely let them battle. Also, get the lady in Veilstone City to massage your Eevee. And if you have access to the Ribbon Syndicate, get a spa treatment.
Edit:
About getting the Soothe Bell, you can get it from a maid in Mr. Backlot's mansion in D/P/P.
In FR/LG, you get it in the Pokémon Tower. It's hidden where Mr. Fugji stood.
In R/S/E, you can get it in the Pokémon Fan Club, I think.
I'm not sure where you get it in G/S/C, though.