Linda-

I'll also look forward to what you come up with.

My understanding is that banjos went to sea during the minstrel craze which swept 19th century North America from the late 1830's on. Some of the shanties themselves were adapted from minstrel songs as Doerflinger and Hugill point out. Here's a great example from SHANTIES OF THE SEA SEAS, p. 256:

Gimme de Banjo

This is the day we make our pay-day,
Dance, gal, gimme de banjo!
Oh, that banjo, that seven-string banjo,
Dance , gal, gimme de banjo!

Haul away for Campeachy Bay...
Oh, haul away an' stretch out yer pay-ay...

A dollar a day is a buckera's pay...
Oh, bend yer high shoes an' lavender breeks, boys...

There's my Sal, she's the gal for me, Boys...
Oh, I know that she'll be a-waiting for me-e...

I'll bang on the banjo -- to show her my love-o...
Oh, that banjo -- that ping-a, pong-a banjo...

Another shanty but from the West Indies (Harding of Barbados) also makes explicit reference to the banjo, from SHANTIES OF THE SEVEN SEAS, p. 274:

Coal Black Rose

O, me Rosie, Coal Black Rose,
Don't ye hear the banjo
Ping-a-pong-a-pong?
On, me Rosie, Coal Black Rose!

O, me Rosie, Coal Black Rose,
Strung up like a banjo,
Taut an' long,
On, me Rosie, Coal Black Rose!

O, me Rosie, Coal Black Rose,
The yard is now a-movin',
Hauley-hauley, ho!
On, me Rosie, Coal Black Rose!

O, me Rosie, Coal Black Rose,
The Mate he comes around, boys,
Dinging an' a dang!
On, me Rosie, Coal Black Rose!

O, me Rosie, Coal Black Rose,
One more pull, boys,
Rock an' roll' er high!
On, me Rosie, Coal Black Rose!

Cheerily,
Charley Noble