It's not possible to evolve Eevee into Espeon or Umbreon in Pokemon FireRed or LeafGreen, because there isn't an internal clock running.
However, it is possible to evolve Eevee into Espeon or Umbreon on Ruby, Sapphire, and Emerald. As long as Eevee has high happiness, it can evolve into Espeon between 12:00 PM and 11:59 PM, and Umbreon in between 12:00 AM and 11:59 AM. Please note that the clock needs to be running (the battery needs to be working) in order to be able to choose. If the battery is dead on your game, the time it is on your clock in your house will tell you what Eevee can evolve into.
EDIT: I forgot to mention, you can also get both Espeon and Umbreon as your starters in Pokemon Colosseum. You can trade them over to your 3rd gen cartridge to have them on your game.
Source: Knowledge and experience