If Clancy-Makem are the ultimate source of "Ballygrant," they seem to have had a deeper insight into the geography of the area than one might expect.

Regardless of that, if "baile cuain" means "quiet town," the connection with Ballygrant - as likely as it may be geographically - starts to look like a rationalization or a coincidence, no matter who first placed it in the song. Surely there were several "quiet towns" separated by water from Carrickfergus?

The nature of the evidence (phonetic Irish from ca1840, and not necessarily a completely accurate representation) suggests that it's impossible to know either way.