How would privately minted coins enter circulation? I read a great article about private minting in early America that talks about some of the private minters whose copper, silver, and gold coins were widely circulated throughout the country without the federal government having anything to do with the process. I had some questions about how exactly that would work, so in the absence of a historian, I thought I would ask here for some answers that would have to make sense economically.

These coins would have to be considered commodity money rather than fiat money since the government wasn't involved. In order for this to work, would the face value of the coins have to be really close to the intrinsic value?

If the face value and intrinsic value were the same, how would the minters profit without any seigniorage?

Without a central bank, how would money minted by private minters enter circulation?
I am unsure about the American situation, but I learned a bit of history about token issuance in pre-Confederation Canada. These comments are based on the notes in a token collector guide.
Since they were privately issued, they would be called “tokens” and not “coins,” as that was reserved for governmental issuance.
In the Canadian colonies, there was a deficiency of low denomination copper coinage, which were officially minted in Britain (and British governors did not really  care). So the locals took matters into their own hands.
The banks were serious about coinage, and the metal content was close to what was implied by face value. Non-banks also issued tokens, but the metal content was quite often below face value. The banks did not like these tokens, and they typically did not accept them at face value, and melted them down. (This means that the tokens with the least copper are the rarest, and worth the most now.)
The tokens entered circulation via being handed out by the firms that minted them. Even if the tokens were too dodgy to be used elsewhere, people could return them to the same shop.