It is quite possible that these books, published in the 1700s, found their way to America. But I doubt that any ballads entered the oral tradition in America directly from them.
"WIT AND MIRTH: or Pills to Purge Melancholy; being a Collection of the best Merry Ballads and Songs, Old and New. Fitted to all Humours, having each their proper Tune for either Voice or Instrument: most of the Songs being new set." By Thomas D'Urfey. 6 vols. London. 1719-20.
"THE TEA-TABLE MISCELLANY: A Collection of Choice Songs, Scots and English." Edinburgh. 1724. 4 vols. [Glasgow, R. & A. Foulis. 1768. 2 vols.]
RELIQUES OF ANCIENT ENGLISH POETRY: Consisting of Old Heroic Ballads, Songs, and other Pieces of our Earlier Poets; together with some few of later date. By THOMAS PERCY, Lord Bishop of Dromore." 3 vols. 1st ed. London, 1765. [4th ed. (improved) 1794.--London, L. A. Lewis, 1839.]
"ANCIENT AND MODERN SCOTTISH SONGS, heroic Ballads, &c." By DAVID HERD. 2 vols. Edinburgh, 1769. 2d ed. 1776. [3d ed. Printed for Lawrie and Symington, 1791.]
"A SELECT COLLECTION OF ENGLISH SONGS, with their Original Airs, and an Historical Essay on the Origin and Progress of National Song." By J. Ritson. 1783. 2d ed. with Additional Songs and Occasional Notes, by Thomas Park. London, 1813. 3 vols.
"SCOTISH SONG. In two volumes." JOSEPH RITSON. London, 1794. And other Ritson books.
Is there any documentation on these books being in America in the 1700s? And does anyone know of an instance when a ballad passed from such a book back into the "oral tradition" - prior to the middle of the 20th century, when all kinds of "folks" were learning ballads out of books.