By 1684 nobody would have been making coded satirical songs about Charles II: he was dying, he had made himself at least reasonably acceptable to the majority of the British population, and his heir was the important issue.

The accession of James II&VII was hugely controversial, so he was a much more song-worthy subject. If the song encodes something about him (and you had to be circumspect or you'd get the sort of treatment Assange is currently getting), it must predate Monmouth and Argyll's attempted coup, as any satirist would have had to refer to it somehow.

I think the underlying message is that Protestant London is personated as the poor-but-honest maid, while James/Edward is shown as trying to seduce her with the excess and finery of Catholicism. Looking at other broadsides by the same authors might help to crack the code.