On the (fairly safe?)assumption that at least some immigrants were Scottish, you might try "The Scots Musical Museum" (six volumes, 1787-1803, volumes two, three, four and five edited largely by Robert Burns) to see if there are any likely choices; there's a twentieth-century reprint. From 1769 and 1776 there's David Herd's "Ancient and Modern Scotish Songs", which might yield something, and Hans Hecht's "Songs from David Herd's Manuscripts", published c.1900. Although the title of Allan Ramsay's "Tea-Table Miscellany", 1724 and often reprinted, indicates that many of the songs therein were (as he put it) written by some "ingenious young gentlemen" of his acquaintance as well as himself, you might find something suitable. Only the SMM has music, though I think Ramsay's book at least gives titles of airs. Good luck.