How do I get the coin case?

You can get the coin case from a man in the Celadon restaurant at the top left corner.

To get the coin case in Pokemon blue simply go to the bar and talk to the man that lost it all in the slots. He will then present you with the coin case.
Luna

Go to the restaurant in celadon. In the top-left corner, there will be a guy. He will say not to laugh. Then, he will say I blew it All at the slots and say I don't need this and give you a coin case.

Find a man who might be old and he will give you a coin case

In Celadon, underneath the game corner, there are two buildings with doors. Enter the first one, and in the top left corner there is a man. Speak to him to get the coin case.