Songs in Journals pre-1850; Gale Huntington, 1964 and reprints, "Songs the Whalemen Sang," Barre Pub., Dover and Mystic.
Songs found in logs.
Songs of the 1850s should be included.
This list is to remind me to look for other versions and variants of songs sung on ship c. 1850. Some may have been sung by the common seaman.
Of course there are the songs of Charles Dibdin and Charles Dibdin Junior, and many others, but many would have been forgotten by 1850.

The Coast of Peru, 1832
The Whalefish Song, 1849
The Greenland Whale, 1833
The Cruise of the Dove, 1845
Our Old Friend Coffin, 1846
The Wounded Whale, 1836
The Ship Euphrasia, 1849
A Wet Sheet and a Flowing Sea, 1844
Sling the Flowing Bowl, 1839
Loose Every Sail to the Breeze, 1795
Captain James, 1768, 1840, etc.
The Topsail Shivers in the Wind, 1876, 1835
The Sequel to Will Watch, 1847
Will Watch, ?c. 1820
The Sea, 1847
Saturday Night at Sea, 1843
I Was Once a Sailor, 1843
Hearts of Gold, 1832
The tempest, 1827
The Can of Grog, 1776
The Pirate of the Isles, 1847
The Demon of the Sea, 1847
The Rover of the Sea, 1849
Most Beautiful, 1837
The Sea Ran High, 1833
The Ocean Queen, 1845
Neptune, 1848
The Dauntless Sailor, 1808
The Sovereign of the Sea, 1776
A Life on the Ocean Wave, 1847 (But much earlier)
Covent Garden, 1828
Cupid's Garden, 1767
William Taylor, 1817
The Tarry Trousers, 1847
The Captain Calls All Hands, 1832
A Young Virgin, 1817
The Nobleman's Daughter, 1840
John Riley, 1847
The British Man-of-War, 1847
Pretty Sally, 1845
The Beggarman, 1845
Bright Phoebe, 1847
The Dark-eyed Sailor, 1847
Our Ship She Is Lying in Harbour, 1847
The Silvery Tide, 1847
The Ship Carpenter, 1767
The Lily of the West, 1844
Lovely Caroline, 1845
The Turkish Lady, 1768
The Times, 1804
The Sons of Liberty, 1790
The Lass of Mohee, 1847
The Heathen Dear, 1832
The Moon Is Brightly Beaming Love, 1847
Shearing Day, 1832

(More to come)