Here's a list of old-time tunes from the Dallas Morning News of Aug. 28, 1927.

The tone of the article suggests that most all of them are from the 1890's or earlier. ("Red Wings" [sic] is one exception.)

Fine Times at Our House (or "George Booker")
Sallie Gooden
Arkansas Traveler
Gwine to the Weddin' with Sallie Ann (or "Great Big 'Taters in Sandy Land.")
Sugar in the Coffee
Haste to the Wedding
Billy in the Low Ground
Bonaparte's Retreat
Gray Eagle
The Campbells are Coming
The Fisher's Hornpipe
Molly, Put the Kettle On
Dan Tucker
Sallie Johnson
The Mocking Bird
Wagoner
Snow-Bird on the Ash Bank
Hell Among the Yearlings
Cotton-Eyed Joe
Seamus O'Brien
Soldier's Joy
Durang [sic] Hornpipe
Mississippi Sawyer
The Downfall of Paris
I Love Somebody
Texas Quick Step
Forked Deer
Eighth of January
Rickets [sic] Hornpipe
Sailor's Hornpipe
Red Wings
Walk Along, John
Hickman Rag
Dill Pickle Rag
Nigger in the Wood Pile
Devil's Dream
Done Gone
Indian Eat the Woodchuck
Leather Breeches
Silver Bell Waltz
Run, Nigger, Run
Old Molly Hair [sic]
Buffalo Girls
Rabbit, Where's Your Mamma?
Give the Fiddler a Dram
When You and I Were Young, Maggie
Rye Straw
The Old Bell Cow
Jimmy on the Railroad
Pop Goes the Weasel
The Old Gray Mare
Life on the Ocean Wave
Over the Waves
Bonnie Blue Flag
Take Off Your Overcoat and Throw It at the Ladies
Kitty Clyde
Natchez Under the Hill
Zip Coon
Turkey in the Straw

A few more titles from the same paper in 1900:

Pendleton's Reel
Culpepper
Possum Up a Gum Stump
Gilroy [sic]
Black-Eyed Susie
Girl I Left Behind Me
Banko
Yankee Doodle
Melinda
Rory O'Moore
Hell Broke Loose in Georgia
Dixie
Siege of Knoxville
Flowers of Edinburgh
Kingdom Come
Old Black Joe
Suwannee River
Drunkard's Lament
Black Jack Grove
Home, Sweet Home

All these tunes were known in Texas.

I posted another, shorter list, also from Texas in 1901, on the "Opinionated Civil War" thread. It offers a few additional titles.