Apparently, I have one banknote from Argentina & one from Nepal. These are the only countries (at least, judging by comparing the “My Collection” maps) where I have notes but no coins.
I suppose I could argue for England, Scotland, Wales, and Northern Ireland as I have banknotes from their commercial banks (though England & Wales have no surviving ones today), but none of them issue or issued coins.
But I do have a large expanse of UK coins, which of course circulate in all the home countries. Funny how Numista ranks the coins as UK, but all notes as the home country (including the central bank, Bank of England, notes which are apparently “England” despite being the currency of the entire UK and all the issuing commercial banks are backed fully in BOE notes). But that's probably splitting hairs.