The broadside of c. 1690 is titled "Barbara Allen's Cruelty, or the Young Man's Tragedy; with Barbara Allen's Lamentation for her Lover and Herself, to the tune of Barbara Allen." This copy, preserved in the Roxburghe Collection II, 25, is a stall ballad printed for "P. Brookeby, J. Deacon. J. Blare, J. Bach." Chappell who edited the collection, considered this copy contemporary with Pepys.
That the broadside is to be sung to the "tune of Barbara Allen" proves that at that time (c. 1690) Barbara Allen was a known and circulating ballad with a tune. Thus it predates c. 1690.
Inquiry into the history or the publishers listed reveals that the broadside was probably printed between 1683, when Joseph or Josiah Blare Mean to do business in London and 1696, when Philip Brookaby ceased to do business as a bookseller. [Henry R. Plomer, A Dictionary of Printers, 1922]
Richie