The short answer is that anything copyrighted before 1922 is now public domain; that is, the copyright has expired. For further info, see Public Domain Information Project

That site gives good detailed information about copyright law. It also lists titles of many songs that are in the public domain. But it doesn't give words or music.

This site: Public Domain Music -- gives music in the form of Midi files. If you have the right kind of software, you can convert a Midi file to a printable score.

Neither of these sites classifies any songs as "country." You will have to figure that out for yourself.

Many of the songs in the Digital Tradition are free of copyright, but you will have to do further research on each one to find out how old it is. See the Mudcat FAQ - Newcomer's Guide for information about how to search for songs.

Two other good sources of music are The Lester S. Levy Sheet Music Collection and The Library of Congress 'American Memory' Collections.

Anything by Stephen Foster would fit your criteria of popular, country, and copyright-free.