Jon,I learned this chantey from Joanna Colcord's collection "Roll and Go" which is devoted to American chanteys. The only recording I know of is a disc by Forebitter, a chantey group based at Mystic Seaport Museum. They've released an anthology of American chanteys. You can contact them at craig@mystic.org.
Here are all the verses I know:
Today is the day we pick on the banjo. Dance, gal, gimme the banjo! Oh, that banjo, that 7-string banjo. Dance, gal, gimme the banjo! Oh, that banjo, that talla talla wango. Dance...
When I was just one and twenty Dance... I had gals and money a-plenty. Dance... Oh, that banjo, that talla talla wango. Dance... (these two lines repeat at the end of each verse)
I was sent to school to be a scholar. My collar was tight and I could not swaller.
That's my book there on the table, You can read it if you are able.
I think Stan Hugill gives a version in his Shanties of the Seven Seas. I don't know how to do tunes on this rig yet, so I can't help you there. The books and the recording can supply that for you.
Jerry