Finding chords to folk tunes isn't too tricky, the theory is pretty straightforward- there are 3 major and 3 minor chords in any diatonic scale, which pretty much covers all eventualites. Finding a stylistic approach that's wise to the subtleties of rhythm and melody, that's the real challenge.

The "correct" chord isn't necessarily the "right" one. Sometimes the chord is so obvious that playing it adds nothing, and sometimes there isn't a right chord at all.