Some more that occur to me (sorry if others have already entered them while I've been typing). Note that, for some of them, you have to stretch your definition of "country" a bit.
Confederate States of America, 1861-1864. Popular, beware of fakes.
Katanga (seceded from Congo), 1960-1963. Much more expensive than the notes of fellow secessionists Biafra.
Krajina, Serbian-occupied part of Croatia during breakup of old Yugoslavia, 1991-1995.
Memelland, also known as Klaipeda - a small neutral state on the Lithuanian-German border, 1919-1924. The notes are listed in Pick, though they really should be classified with all the other German notgeld.
Qatar & Dubai, short-lived monetary union, 1966-1971.
Rhodesia & Nyasaland, a federation of the future Zambia, Zimbabwe and Malawi, 1953-1963.
Saarland, French-occupied Germany, 1947-1957. The "mark"-denominated notes actually date from a different, earlier time period to the "franken"-denominated coinage.
Srpska Republic, the Serbian half of Bosnia-Herzegovina, during Bosnian war 1991-1995
Texas (independent republic), 1836-1846. Even pricier than CSA notes.
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