I'm a big fan of the traditional cowboy genre, and these are songs that I've found that fit in the group. If you like them, enjoy. They are mostly pretty easy for guitar or mandolin.
Michael Martin Murphey, Misc. Cowboy, Marty Robbins, Don Edwards, Johnny Cash, Emmylou Harris, Roy Rogers, Red Steagall, Waylon Jennings and Merle Haggard