I agree with the Codger.   There are a lot of ways to make a 2 or 3 chord instrumental background more interesting, with passing cords, modulations (e.g., shifting from the major to the 7th in places), doing melody runs, etc.   
In fact, I had been playing Jambalaya for years before I heard someone mention it had only two chords and discovered it actually did. It's so easy to play the melody on Jambalaya, on guitar in the key of G, anyway, that I seldom actually played the full chords, but mainly did Carter-family style melody runs, sometimes hitting two strings at once.   (It might be harder to do that on a uke or in some other keys.)