"Dundee, it is a pretty place, Surrounded by a wall, Where brave Argyll did won the field With sword and cannon ball."
This seems to be known only as a "choir rhyme" in the Sam Henry collection, from 1924, used to teach choirs a tune when, as Presbyterians, they were not supposed to sing the actual words. Normally, this would not be reason to consider the piece traditional.
This text, however, or at least the first three lines, are known from Hunt's 1634 psalter, and they are also similar to lyrics in "The Earl of Errol." That says to me that this stanza, in some form or other, kicked around in tradition.
I'm not sure which battle is described in this song. Logically, one would guess that it's Archibald, eighth Earl and first Marquis of Argyll (1598-1661) -- but his military feats as a Covenanter came *after* 1634.
Archibald's father Archibald, the seventh Earl (d. 1638) was also a soldier, though his success was mixed, but he did his campaigning in the Highlands.
The other Earls of Argyll, insofar as I can follow their careers, are no better candidates (e.g. the fifth Earl was Mary Stuart's field commander at Langside, but that was a lost battle nowhere near Dundee).
Two battles are listed as taking place in Dundee, but they are dated 1645 and 1651 -- again, after the date of the psalter describing Argyll fighting at Dundee. - RBW