You will receive the Coin Case in Veilstone City from a Clown NPC who resides in a house directly to the west of the Game Corner. You’ll just have to play a small game with the NPC and he’ll give you the Coin Case for free.
There are also no prerequisites here, so as soon as you reach Veilstone City just speak to the Clown and play his coin game.
It might take a couple guesses to win his game, but it’s really easy & you’ll get his Coin Case as a reward.
Getting the Coin Case (Step-by-Step)
To find the Clown who has the Coin Case, first get to Veilstone City and move south from the Pokémon Center.
Stick with the main street as it turns to the west.
Continue traveling west until you reach the southwestern corner of town.
Turn up some stairs at the very western edge of town.
Climb the stairs and take a right turn in front of the two blue houses.
Enter the house on the right.
Inside the house are two NPCs who claim to be performance artists.
Speak with the Clown NPC.
The Clown will perform a coin trick for you. At the end of his trick, he will ask you which of his closed hands his coin ended up in, left or right.
Pick any hand (there’s not much strategy here).
If you choose incorrectly, speak to him again and pick the other hand.
When you’ve found the coin then the Clown will reward you with the Coin Case.
Coin Case Details and Uses
The Coin Case allows you to hold Coins, which you can earn from the Veilstone Game Corner. The case holds up to a maximum of 50,000 Coins in total.
Coins are used both for playing the Game Corner’s slot machines, and for buying TMs and items at the Prize Exchange building next door.
Without the Coin Case you’ll miss out on a few exclusive (and powerful) TMs that are only available via the Veilstone Game Corner – this includes TMs for moves like Explosion, Giga Impact, and Gyro Ball.
To check how many Coins you have, just select the Coin Case from the Bag at any time.