Not quite as old:

Songs of American Sailormen
Joanna C. Colcord
1938

Abram Brown
Across the Western Ocean
Alabama
Andrew Rose
A-Roving
Bangidero
Banks of Newfoundland, The
Believe Me, Dearest Susan
Billy Riley, O!
Black Ball Line, The
Blow, Boys, Blow
Blow the Man Down
Blow, Ye Winds
Bold Daniels
Boney
Boston
Boston Come-All-Ye, The
Bottle O!
Captain Kidd
Cheerly, Man
Clear the Track
Coast of Peru
Codfish Shanty, The
Constitution and Guerriere, The
Can't You Dance the Polka?
Countersigns, The
Cruise of the Bigler, The
Derby Ram
Diego's Bold Shores
Dom Pedro, The
Dreadnaught (Dreadnought), The
Drei Reiter Am Thor
Drunken Sailor, The
Fair Princess Royal, The
Fire Down Below
Flying Cloud, The
Franklin's Crew
Galloping Randy Dandy O!
Girls Around Cape Horn, The
Golden Vanity, The
Good-bye, Fare You Well!
Goodbye, My Love, Goodbye
Greenland Fishery
Hanging Johnny
Haul Away, Joe
Haul on the Bowline
Heave Away
Her Bright Smile
High Barbaree
Highland Laddie        
Hog-eye Man, The
Home, Dearie, Home
Huckleberry Hunting
Hundred Years on the Eastern Shore, A
In de Mornin'
Jamestown Homeward Bound, The
John Cherokee
Johnny Boker
Johnny Come Down to Hilo
Juley
King Edwards
Lass of Mohea, The
Leave Her, Johnny
Liza Lee
Long Time Ago, A .
Lowlands        
Mademoiselle from Armentieres
Mobile Bay
Old Sailor's Song
One More Day
Paddy Doyle
Paddy Get Back
Paddy Works on the Railway
Persia's Crew, The
Poor Old Man
Retour Du Marin, Le
Reuben Ranzo
Rio Grande
River Lea, The
Rocks in de Mountens
Roll the Cotton Down
Rolling Down to Old Maui
Rolling King
Round the Corner
Row, Bullies, Row
Rules of the Road
Run with the Bullgine
Sacramento
Sailors' "Come-all-ye"
Sailor's Grave, The
Sally Brown
Santy Anna
Shallo Brown
Shenandoah
Shenandoah, The
Sindbad
Sing Sally O!
Slav Ho!
Snapoo
So Handy
Stately Southerner, The
Stormalong
Ten Thousand Miles Away
There She Blows!
Tom's Gone to Hilo
Up She Goes
Whiskey Johnny
Ye Parliament of England
You Gentlemen of England