Some quick thoughts

The Water is Wide is often labelled as American
Scarborough Settlers Lament is Canadian with a Scottish melody
Fireside Book of American songs lists Banks & Braes and Barbry Ellen

Folk Songs of Old New England has quite a bit including
Over the water to Charlie,
Gypsy Daisy (Seven Gypsies),
Jenny Jenkins (Will you wear Red) is a kids songs from Galloway
Our Goodman (seven nights drunk) This shows up in some 18thc Scottish collections
Three Crows (Twa Corbies)
more

American Songbag has some
Who will shoe your pretty little foot (Fair Annie of Lochryan)
Weevily Wheat
Gypsy davey
The Brown Girl
more

Cowboy songs are a good source
Roll on little dogies has the same tune as "My Bonnie"

A lot of Stephen Foster's stuff sounds suspiciously Scottish

Good luck and let us know what you end up doing

cheers- Julia