Most countries simply aren't big enough and/or don't have a large enough economy to make having their own mint a viable prospect. They contract out their coinage requirements to larger foreign mints, both government-owned and private corporate mints.
For circulation coinage, you need a large, high-capacity mint.
The Royal Mint,
Royal Canadian Mint, South African mint and others are among the major players in world coinage supply. Note that some countries switch suppliers from year to year, depending on which mint offers then a better contract. New Zealand, for example, has had their coins struck by Canada, South Africa, Australia and
The Royal Mint in past years.
NCLT (collector) coinage is a different story; here, the private and corporatized mints tend to dominate. Note that, for some mints in some countries, it is the mint themselves, rather then the country that is allegedly issuing the coins, that is the instigator and promoter of the coins. For example, nobody in Uganda thought of issuing coins to commemorate the Greek mathematician Pythagoras via a triangular "millennium" coin back in 2000 - that was purely a
Perth Mint marketing gimmick. I doubt anybody in Uganda is aware that these coins exist.
As to your question: no, sorry, I'm not aware of a single list outlining which mints struck which kinds of coins for which time periods for each country. But as you can see, such a list would be neither brief nor simple.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis