Analagous to the "rusty trombone", the rusty banjo involves administering analingus to a female while reaching around and strumming her clit/pussy... thus effectively playing the "banjo" with her genitals.
The term rusty generally refers to the "rusty" coloured anus area.
Man, last night I was over Kelly's place and I gave her a rusty banjo!! She went CRAZY while I was flicking her clit and busting out a massive banjo masterpiece with my fingers whilst licking her gorgeous asshole!! :D