A lovely little early fingerstyle composition for the banjo by Frank B. Converse, from his 1865 New and Complete Method for the Banjo With or Without a Master.
Another Frank Converse tune on fretless banjo - this one from 1865. [more inside]
Not the old-time tune you may be thinking of. Fretless banjo with a percussion loop. (As it happens, Garageband's Jazz drum kit instrument has a rattle that sounds a lot like a jawbone.) [more inside]