For guitarists who like the jazz chords from that era I can instantly recommend Ragtime Cowboy Joe as a pop song from mid twenties and Yip Harburg's classic 'Brother Can You Spare A Dime' - plus 'Nobody Wants You When You're Down and Out'. You could try a country version of 'Minnie The Moocher'

Or for something unusual try the original version of (Canadian) Smilin Billy Blinkhorne's 'Poor Ned Kelly' or the more hillbilly 'The Newtons Are Shootin Again'.

Regards, John