There are several very different songs called Banks of the Clyde. This one is a version of William and Jane on the Banks of the Clyde, which appeared on broadsides in the later 19th century.

Several copies from Brereton of Dublin (late 1860s), poorly printed and with his usual idiosyncratic typesetting, can be seen at  Bodleian Library Broadside Ballads:

A new song call'd William and Jane on the banks of Clyde

A much better edition from the Glasgow "Poet's Box" (1856) can be seen at  Murray Collection of broadside ballads:

William and Jane

Not a very well-remembered song, it appears; there is an Ulster set (subtitled One Fine Summer's Morning) in Sam Henry's Songs of the People, and Seamus Ennis recorded a version in Kirkcudbright, Scotland, in 1953. Doubtless there are other examples. Where did you hear this?