Yes you can,
But it's kinda tricky.
You will need Eevee (if you have evolved it, it's OK) and Ditto, and a Rainbow Pass.
Then, travel to Vermilion City, and use the Rainbow Pass at the SS. Anne's location to get to Sevii Islands.
Go to Island 4.
There is a Pokemon Daycare that is capable of holding two of your pokemons.
Give the woman inside your Eevee and your Ditto.
Go for a Bike Ride, Battle Trainers for a while (max 5 min)
Go back to Island Four.
Talk to the man outside the Pokemon Daycare.
He should say, that there is an Egg.
Take the egg.
Place it on your first slot on your Six Pokemon's.
Ride across the map with your Bike. (it takes about 9180 Steps to hatch)
And then, you will have a lvl 5 Eevee!
Good Luck!! ^^
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If you breed an Eevee with a Ditto, then you can evolute the hatchlings into the other forms
There are 7 ways to evolve Eevee. Eevee's evolutions are Flareon, Jolteon, Vaporeon, Espeon, Umbreon, Leafeon, and Glaceon.
eevee can evolve into vaporeon, jolteon, flareon, espeon, umbreon, leafeon, and glacieon.
Her are all eevee's evolutions and how to get them: Jolteon: Use Thunder Stone Vaporeon: Water Stone Flareon: Fire Stone Umbreon: Make happy and evolve during night Espeon: Make happy and evolve during day. If you need any help feel free to message me. :)
All of Eevee's evolutions are Flareon which is a Fire-type and it requires the use of a Fire Stone on Eevee in order for Eevee to evolve into it, Vaporeon which evolves from Eevee once a Water Stone is on it. Vaporeon is a Water-type. Jolteon, an Electric-type which evolves from Eevee once a Thunderstone is used on it. Umbreon, a Dark-type which evolves from Eevee via level up once it's night time and it's happy enough. Espeon, a Psychic-type which evolves from Eevee via level up once it's day time and is happy enough. Leafeon, a Grass type, it will evolve from Eevee once you level it up by the Moss Rock. Glaceon, an Ice type, it will evolve from Eevee once you levelit up by the Icy Rock. Sylveon, a Fairy type and it will evolve via level up from Eevee once it has 2 hearts in Pokémon Amie for affection and it also needs to have a Fairy-type move among one of its moves. Eevee learns Fairy type moves at Levels 9, 20 and 29.