1. I guess you are in Mauville, right? Before that, go back to slateport city.Go to the Pokemart(not the place that have baloons and stuff) and buy a Harbor mail. It just cost 50$, so it isn't very expensive. 2.Go back to Mauville. Beside the game corner, there is a house with a girl siting inside. Talk to her. She will say:"Oh, that's a harbor mail! May I trade it for this coin case?" Surely, YES. She will give you the coin case. Voila! Here's your coin case! have fun playing!:P
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you buy it in the game corner with coins after you get the coin case
So you can get the coin case from the lady in Mauville City.
In Mauville city
go to slateport store and buy a harbour mail then go up to mauville city and go in to the house right of the casino and trade the mail for a coin case to the lady
Amulet Coin is a Hold Item, and Blue version did not have the capabilities of attaching Items to pokemon. Gold, Silver and Crystal were the first games to come up with the Amulet Coin, and you can not transfer to blue via Pokemon Stadium 2 Color Case and Metal Case.