Here is some information that may help date the chanties in ON BOARD THE ROCKET, by Robert C. Adams. This letter suggests that it was 1868. Here is the link:
http://books.google.com/books?id=JVosAAAAYAAJ&pg=RA9-PA7&dq=%22Capt.+Robert+C.+Adams%22&lr=&cd=20#v=onepage&q=%22Rocket%22&f=fal