I believe that you have to get the eevee to max happiness ( or really high ) and level it up in the nighttime. Which is some time from past 6 o'clock on your pokemon clock, to sometime in the morning.
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Train your Eevee at night and with happiness. It will eventually evolve into Umbreon.
Eevee doesn't evolve into Umbreon with a stone. Eevee evolves into Umbreon when it is levelled up with high happiness during the night.
You can get an umbreon by getting an eevee from bill in goldenrod city (in a house) and then you can evolve eevee into umbreon by making it happy and leveling it up at night time.
To make Eevee evolve into an Umbreon, you have to level it up with high happiness at night.
You will need to have your Eevee to full Happiness, then level it up at least once during the night to evolve it into Umbreon.