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Trade Eevee to Sapphire version (if you have the national dex on both games, and completed Celio's sidequest on Leaf Green) then tame it enough until it's happy enough to evolve...and it has to happen during daytime hours to get Espeon.
I think I heard that to evolve it into Espeon in R/S/E you have to evolve it from 12pm-12am, Umbreon is 12am-12pm. That's what my sister done and it worked.
Ok, this is answered, and answered very well if I say so myself.
Next time you have a question ask it in Simple Questions. The link to this overly helpful thread is in my sig and in the group of stickies near the top of the FR/LG (GBA) thread listing.