WorldCat.org shows a catalog listing for sheet music described thus:

SWIFTLY GOES THE OYSTER BOAT : NEW NEGRO MELODY
"Composed and Sung with great applause by W. R. Barlow, The Celebrated Banjoist"
London: Blackman [ca. 1850]

But it is not viewable online, and the only library known to have it is:

Staats- und Universitätsbibliothek – Sondersammlungen [State and University Library – Special Collections]
Hamburg, 20146 Germany