I've added music from Riley's Flute Melodies on my Huddle Workspaces (not sure how that works) but I thought I would add it here,also.
Here are the promised copies of familiar (and a few not so familiar but I liked the titles from the De Capo reprint of the 1814 and 1820 Editions of Riley's Flute Melodies. Some of the songs included are:
Fisher's Hornpipe
The Irish Washerwoman
Rakes of Mallow
Durang's Hornpipe
The Girl I Left Behind Me
Money Musk
Come Haste to the Wedding
Spanish Fandango
Robinson Crusoe
Heaven Rules the Waves, Good Men Never Will Be Slaves
Irish Dance
Drink to Me Only
Rose Tree
The Flowers of Edinburgh
Boatman
Gilder Roy
College Hornpipe
Richer's Hornpipe
Duvil's Hornpipe
Carolan's Receipt
Negro Dance
This last one looks like it might be one of the earliest transcriptions of banjo music. It really lays well on the banjo-It was the "The ?" in the tab I scanned. As you can see, all these tunes were familiar enough to be included in Rileys and the modern versions sound very similiar.