How would a private currency make a profit?

There’s probably a really, really simple answer to this that I’m overlooking. The idea makes a lot of sense, but how would it be profitable? Would it generate interest in the bank that produces it [the currency]? Would those banks charge a fee to businesses who use their currency, because its stability in turn attracts customers?

Let’s see now… I’m a mine. I sell my gold to a mint. The mint makes that gold into coins. It then can use that money… well… to purchase stuff.

In other words, there’s a reason why people counterfeit money.

If you are speaking of money (rather than currency) then there is no profit to be made - it is a common means of exchange, not a product. Currency (coins and such), on the other hand, would have a higher face value than the money-content because of the value of it being pre-measured and insured by the issuer.