There was a 1659 printing of this ballad, according to a Percy society reprint of 1840 which is available in full on the internet archive - Early English poetry, ballads, and popular literature of the Middle Ages ; (1840)
http://www.archive.org/stream/earlyenglishpoet15perc/earlyenglishpoet15perc_djvu.txt
It's in the section "The Crown Garland of Golden Roses, Part II".
As this date was even before the restoration, it's unlikely the ballad was referring to James II.