The singer sees the Armagh coach arrive; one of the passengers is a beautiful girl. He steps up to her, point out his family's wealth, and asks if she will come away with him. She says that she is not wealthy and is pledged to another
I have found no references to "David's Fountain" or "David's Flowery Vale" in maps of Ireland. There are, however, some clues. The lad and lass look at ships sailing to Chester (in western Britain). She comes from Hamiltonsbawn, and is riding the Armagh coach.
Hamiltonsbawn is almost due east of Armagh, half a dozen or so miles from the city center. It is not on any body of water. Armagh isn't on anything navigable, either. But the road from Armagh to Hamiltonsbawn heads on in the general direction of Belfast. Thus it seems likely that David's Flowery Vale is somewhere on the shores of the Belfast Lough. - RBW
Leyden: "John McCance, the owner of this splendid mansion [near Belfast], was born in 1772 and lived until 1835.... The song is correct in mentioning McCance's dwelling at the foot of Divis Mountain: he lived at Roselands on the Upper Falls before moving to Suffolk House in 1811." - BS