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:
The Irish Washerwoman
Rakes of Mallow
The Girl I Left Behind Me
Come Haste to the Wedding
Heaven Rules the Waves, Good Men Never Will Be Slaves
Drink to Me Only
The Flowers of Edinburgh
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.