Funny that you ask this question. I got coined at Orgins last week.
We were talking to a nice young gentleman who is responsible for this: https://www.facebook.com/CastlesAndChemo and in the course of the conversation I asked him if he was Air Force or Army.
To answer the question he pulled an AF coin out of his wallet and slapped it on the table. I haven't carried a coin around since well before I retired, so I owe him a drink. I intend to pay that debt at GenCon.
In the Air Force coins are given out by units, high level officers and Chiefs, or for special reasons. It's usually a reward or recognition of some achievement. It also shows membership in a specific group, a symbol of camaraderie that you can carry and keep even after moving on to other units. Kinda like a secret handshake.
The only coins I ever bought were some very interesting ones at a shop in Korea.
Noel, if you wanted the same tradition for gaming, I would recommend a die. Say a d6 with a special emblem.
It would be up to you to decide how and who you would award them to. Every tradition has to start somewhere.