Only six euro coins had more than 1,000,000,000 minted, all from Italy in 2002: 1c, 2c, 5c, 10c, 20c and 50c. The 20c was the most, with 1,411,686,000.
I think Mexico doesn't have a single year Billion mint coin yet. There have been some close ups to 3/4 but nothing above that. Seems our coins are made to last. But the main factor would be the GDP and inflation. You can't just print more and more money because it will devaluate because of that, but you can't either stop it from flowing because you would de-capitalize your Country. It is a nasty balance.
Numista referee for the "Viceroyalty of the New Spain" (most of it).
History through coins.
Eli V