State of the Art:
“Contemporary publications and the memories of individuals, in later publications, put the existence of this shanty by the 1860s. The Syracuse Daily Courier, July 1867, quoted a lyric from the song, which was said to be used for hauling halyards on a steamship bound from New York to Glasgow.[2] In 1879, George Haswell was passenger aboard another steamship, from London to Sydney, at which time he noted some of the shanties of the crew. These were published in the ship's own fortnightly newspaper, The Parramatta Sun, and they included a full set of lyrics for "Blow the Man Down." The lyrics take up the theme of a ship of the Black Ball Line, and include the refrains, "Wae! Hae! Blow the man down / Give me some time to blow the man down."[3] Although Haswell's article did not receive wide circulation, it did find its way into the hands of Laura Alexandrine Smith, whose own large collection of sailors' songs, The Music of the Waters (1888), was one of the first to be widely available. Smith reprinted the lyrics gathered by Haswell.[4] She also presented a different version of the song that she herself presumably collected, and which was said to be used for hoisting topsail yards. Its lyrics include reference to a sailor coming home to England from Hong Kong, as well as meeting a girl on "Winchester Street."” [song wiki]
Parramatta (1866)
Devitt and Moore


“The Black Ball Line is mentioned in several sea shanties, such as "Blow the Man Down," "Homeward Bound", "Eliza Lee", "New York Girls", and "Hurrah for the Black Ball Line." [Black Ball Line (trans-Atlantic packet)]

So: Couldn't find the Syracuse Daily or a Kicking Jack Rogers. Smith's notes on Haswell & Parramatta don't line up with the wiki, but I may just be looking at the wrong edition. If it does turn out to be more Pacific in origins, one alternate “Black Ball Liner” might be: James Baines & Co.

PS: Mainsails - Parramatta is the go-to example for a top-o-the-line Blackwall frigate. Check your favorite rigging source.