In C, the John Hurt version goes this way:

 C7   F                       C    C7
     Make me a pallet on your floor
  C7   F                       C    C7
     Make me a pallet on your floor
   C       C7           E7
  Make it soft, make it low, 
          F                  D7
  so my good gal, she won't know
            C         G7             C
  That you made me a pallet on your floor.

I surely hope those line up with the words of the song (from Digitrad). But that C7 into F is the key to the John Hurt version. He also uses an F9 (little finger on the 2d string, 3d fret) for melody there in the F parts.

Good luck. It's a good song.

Bob Clayton