teaflower, you should try out the FireRed hack called ShinyGold, it's a really awesome attempt at remaking the Johto games for the GBA.
You can get your Eevee a haircut in the Goldenrod underground path (a salon in a dodgy path under the city is completely logical) every day, which improves its happiness. Also, you can use the weakest healing items (Potions, Berries, etc.) when it's low on health so that you're able to use multiple and get a higher happiness. Don't forgot checking with the Goldenrod woman who tells you how happy your Pokemon are, and make sure to save your game a lot in case Eevee happens to evolve during night instead of day.
Oh, and the train isn't working till you go and solve that sidequest in Kanto.