Recommend me songs that sound like REM's "Country Feedback"

By REM or otherwise. God, if every REM song sounded like this they'd be my favorite band, dude.

Every response you get will be unsatisfying in some way. I'm not sure there's another song like it.

Nevertheless, and off the top of my head, I'd say it's somewhere in the middle of:
REM - E-bow the Letter
Silver Jews(?) - Secret Knowledge of Backroads
Neil Young - Cortez the Killer
Nick Cave - Straight to You

The REM song is obviously closest. It's the vocals that make it.

If I could be half-cruel, half-nonsensical, I'd say "Mr. Writer" by Stereophonics - similar dirgey chords.

At the time I was convinced that the style of this close to certain aspects of late 80s American Music Club - notably the California album (say Blue and Grey Shirt as a reference point). That fractured, feedbacky texture could also be found in Dylan's Most Of The Time.