A little riff I worked out with my former band.  Works great as an accoustic background.  The notes are all straight eighth notes. 

e--------------------------------------------------------------------
B--------------------------------------------------------------------
G--------------------------------------------------------------------
D--------------------------------------------------------------------
A----8-8---8-8---8----8-8---8-8---8----8-8---8-8---8----8-8---8-8---8
E--6-----6-----6----5-----5-----5----4-----4-----4----3-----3-----3--

Just keep repeating that over and over again.  You can add a clean elctric guitar or another accoustic to play solos over top.  Nothing too loud though, this is a mellow piece.