Eric Weisberg played banjo on Battle of NO and Hootenanny. Mark Pearson played on An American Song. The Brothers Four didn't really have a bona fide banjo player until Mark joined the group. Mike Kirkland strummed a 4-string tuned like the top four strings of a guitar, ala Bob Shane. Mark, and then myself, were the first actual trained banjo players, and, coincidentally, we both learned from Dutch Groshoff as youngsters in Spokane, WA.
I think all the groups used studio musicians to greater or lesser degrees. The Trio was fond of Glen Campbell, and in fact, it was he who played banjo on Desert Pete. Glen doesn't actually play banjo, so what you hear on that song is a 6-string banjo, tuned like a guitar.