1868        Unknown. _The Riverside Magazine for Young People_ (April 1868).

Lighter introduced this early reference to the chanty form of this song.

Learned on "a recent Atlantic voyage."

//
       As I walked out one mornin',
                Down by the Clarence Dock,--
       Chorus. Heave away, my Johnny, heave away!
       'Twas there I met an Irish girl,
                Conversin' with Tapscott.
       Full chorus. An' away, my Johnny boy, we're all bound to go!

       "Good mornin' to yer, Taspcott;
                Good mornin', sir," she said….
       An' Tapscott he was that perlite
                He smiled an' bowed his head….

       "Oh, have yer got a ship," she said,--
                "A sailin' ship," said she,--
       "To carry me, and Dadda here,
                Across the ragin' sea?"

       "Oh yes, I got a packet ship,
                Her name's the Henry Clay,"--
       "She's layin' down to the Waterloo Dock,
                Bound to Amerikay."

       Then I took out my han'kerchief
                An' wiped away a tear,--
       And the lass was that she said to me, [sic]
                So, fare ye well, my dear!

       Some times I'm bound to Africay
                Some times I'm bound to France,--
       But now I'm bound to Liverpool
                To give them girls a chance."
//

Presumably, the fireman's song, being cited as a "slave song," dates from a ways earlier than 1867 (or 1865 - by which time Allen's book was prepared for publication). About the chanty, I don't think we can say.

My "feeling" (based on broad observations, not just this song) is that the fireman's song would have come first, and that the Irish Emigrant ballad (along with other variations) would have been spliced to it.

However, that theory is belied by the fact that these two "earliest" versions share the reference to "Henry Clay." While "Henry Clay" sounds like he might have been a cruel boss (cf. the boss in "Pay Me My Money Down"), it also was indeed a Liverpool-NY packet ship:

http://www.immigrantships.net/v3/1800v3/henryclay18511112_01.html