This question arises from the fanciful notion going around blogs that the Treasury could mint a trillion dollar coin to pay the debt down.
But the original question must have an answer.
If we’re talking about dimes, pennies, etc. (and not specialty coins), they mint as many as the Federal Reserve Bank wants to buy, I believe. And the FRB buys as many as its customer banks want. Obviously, in practice, both levels of demand are forecasted in advance.
I believe in the case of the Presedential and Sacagawea dollar coins they were required to produce certain numbers by Congress - there was little actual demand for them, leading to a 1.2 billion dollar stockpile (I think since that story was written production has been scaled way back, to basically just satisfy the collector market.)
A US Dollar is a Federal Reserve Note, of course. A coin is not. A coin predates the Fed by over 100 years.
What you say would make sense but history shows another decision maker is working.
There’s no suggestion the trillion dollar coin would pay down the debt. It is simply a loophole to avoid the debt ceiling.
Before the Federal Reserve System, retail banks ordered coins as needed from the friendly local mint. Before the late 19th century, though, there was little stndardization, with all kinds of rogue private mints making their own coins.
Now, coins and bills are distributed via the Federal Reserve banks, who get them from the US Mint and the BEP.
So much mis-information, so little time! 
Rogue private mints making their own coins? What are you smoking?
Usually around gold mines in the West, all sorts of minting operations sprouted up, such as those run by Templeton Reid and Christopher Bechtler, but there were a lot of other ones.
OK. Please list what they minted. They minted less than 1/10 1 % of the coinage produced by the Mints of the US. Probably less than 1/1000 %.
Banks got coins from the US Mints.
Whoa! Let’s take 1880 as an example. The US government had two mints making coins, San Francisco and Philadelphia. Philadelphia made 39 Million cents that year.
Philly and SanFRan made half a million dimes. Not enough for commerce.
But, private mints were forbidden to make coins at that time.
It wasn’t rogue, since it was authorized by the provisional government, but there were gold coins minted in Oregon. It was known as Beaver money. Admittedly, it wasn’t a huge amount of coins, but that’s mostly because they were only minted for a short while. Once Oregon became an official territory, it becaume illegal for them to mint coins. But the coins did circulate in the territory until regular US coins became more common.
The surviving coins are extremely valuable, since there are very few left. And most of those have lots of wear, since they were made of pure gold, rather than the gold-copper alloy that specie is usually made from.
Serious question, not a nitpick: What about N’awlins? And was Carson City closed in 1880?
You could always check the wikipages on them. If so, you’d find they were both in operation in 1880.
Sorry. I really screwed that up. Yep, both were going, but both Carson City and new Orleans were only making silver dollars, nothing smaller.
Thanks. I knew there were less-than-dollar coins with “O” mint mark from the McKinley/TR period, and wasn’t at all sure what CC’s dates were. What you said clarifies things immensely!