I don't know about the concertina, but by the 1930s and 50s, lots of western bands used accordions

Among these, were Sons of the Pioneers, Gene Autry & Roy Rogers.

Several contemporary western bends, Lone Prairie has performed at many Cowboy Poetry and Music Gatherings, Such as the Arizona Cowboy Poetry Festival in Prescott, Arizona.

Lone Prairie has a web site: http://www2.cruzio.com/~zozobra/