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/
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sj