More “American country music” even than slide guitar is the pedal steel guitar, though most people might not know what it is by looking at one. If you’re imagining the sound of a country slide guitar, it’s probably a pedal steel.
Others thoughts (with no attempt at correct spelling): Balailaika for Russia, and bouzouki for Greece. I’m afraid I don’t know the names of the mini guitar and extra large guitar/small sideways bass used in mariachi bands, but they’re prototypically Mexican. There are also lots of ‘Chinese’ instruments, which probably even are specific to certain regions (at least to those who know more about them than I do).
The cursed Andean flutes aren’t specifically one country, but a region of three or four. Likewise steel drums I think cover a couple countries in the Carribean. More broadly belly-dancer’s finger cymbals are Middle Eastern.
The tuba isn’t really unique to one country, but it does tend to evoke Germany/Austria or a US town settled by Germans/Austrians.