You have to catch 40 Pokemon and get it from Professor Oake's aide. He can be found in the upstairs observation room in the gatehouse that connects Celadon City and Cycling Road.
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Either its the big building to the left of celadon city or the one left of fuchsia city but at the top of the building an Oak Aide will give you an amulet coin if you registered 40 Pokemon in your pokedex.
In the big building either it's west of celadon city or fuchsia city but there is a prof oak aide inside on the top floor and he gives you the amulet coin if you have registered 40 Pokemon in the pokedex.
West of Celadon city and the north entrance of the bike only path. Go inside, and walk upstairs. Professor Oak's aide will give you the Amulet coin, only after you have caught at least 40 different Pokémon.
In Red the Amulet Coin item does not exist.
You can find an Amulet Coin in the Goldenrod Department Store basement.