For any type of money to work, the minter has to have a product/service that they will buy back the money with. Then the money is a stand-in for that product/service. He who would print and sell money in exchange for something must be willing also to trade something in exchange for his coin. So that the coin represents a voucher from the mint for something the people want.
Maybe the player's minted coin counts as the Leader's coin for his services -- which ain't much. He listens to people bi*ch all day long, and maybe charges for it. "I'll listen to your complaints for a fee." Then he could say one minted coin has a value of one therapy session. People
could accept and trade that, but the problem is that it's not a high volume need for the people. So it wouldn't work very well as a substitute commodity.
Another approach might be to assign who is the minter of coin, and what they promise in return for their coin. Maybe the brewer mints coin in exchange for beers. Or the Carpenter mints coin in exchange for barrels. It should be a common high-demand commodity to make the currency useable by everyone.
Or maybe the governing authority (leader) declares ownership of a base commodity, such as crops. He then pays the farmers in coin, representing one crop each. The farmers can buy crops for their own consumption, or sell the coin to others who might want crops.
Government ownership would let the player mint any amount of coin, but could be in trouble if the dwarves decided to come collect and there wasn't enough crop to cover the coin. Upset dwarves begin a tantrum spiral from inadequately capitalized coin

Maybe they start trading the coin at a lesser value (3 coins/ 2 crops or some such) because that's all the total currency is worth, compared to the total crop available. And voila, we have modelled inflation due to a greedy leader printing up too much currency.