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
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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 and by 1 habor mail then go to the lady's house next to the game center and trade it with her.
First, you get a Harbor Mail. Anywhere. Then go to Mauville. Go to the house east/right to the game corner. Talk to the lady, trade the Harbor Mail and she'll give the coin case