The archtop mandolin is an entirely American innovation. The bowl-back and flat-back versions were European, but the archtop was invented in the US by Orville Gibson.
Similarly, the archtop guitar was also invented by Gibson.
Parlor guitars were invented in the US as a more "family-friendly" version of the larger-bodied guitars ...
Harry Partch's various stringed instruments:
The adapted guitar, refretted to handle Partch's 43-tone scale
The adapted viola: a viola refitted with a cello fingerboard, with bridge modifications to more easily allow triple stops and brads hammered into the fingerboard to make finding the sometimes very close notes in Partch's scale easier
The Harmonic ...
The bass guitar was developed by Leo Fender in America. Riffing off of that, Ernie Ball(working in California) based the acoustic bass guitar off of the Mexican guitarron.
The Appalachian dulcimer, played like a lap guitar, was invented in the eastern US, hence the Appalachian moniker.
Most people keep throwing around the misconception that the Ukulele was engineered in all its (small) glory in the US.
The Ukulele spawned from the adaptation of the Portuguese instrument "Machete" (brought to the island by portuguese immigrants), which, in itself, is an adaptation/transformation of the Original, the "cavaquinho". If you look at it, it's ...
There's the lap steel guitar, developed in about 1935 in Los Angeles by a steel guitar player named George Beauchamp from the Hawaiian steel guitar. This evolved into the modern Pedal Steel Guitar.
There is also the bass guitar which evolved from the electric guitar but is now generally considered to be a different instrument. The first basses were ...
Surely the Banjo.
Used in various forms in folk, bluegrass, trad jazz/dixieland. Even in some pop tunes (in the US and around the world). And it even found a place in traditional Irish folk music.
The resonator guitar should fit the bill as well.