Phil, Google Books displays no readable text and gives the title simply as "A Duett, for Two Performers on One Pianoforte." The British Library copy is not online.
Where do you see the associated title "Corrie Owen"?
" [T]he earliest publication of the tune I can discern was in James Aird's Glaswegian c.1788 'Selection of Scotch, English, Irish and Foreign Airs', Vol 3 where it was issued under the name 'Auld Bessy'. ...Unlike 'Paddy [O'Rafferty]', there's no hint in Aird's publication that he considered it to be of Irish origin. The next two publications that I can confirm are both from Dublin under the name 'The Garyon'; it can be found in 'Cooke's Collection of Favorite Country Dances for the present year 1797' (see Figure 7, middle) and in 'Hime's Collection of Favorite Country Dances for the present year 1797'. The name 'Garyon' was subsequently distorted to 'Cary Owen' [etc.]...each of which appeared in London publications of the tune around the year 1802. The tune was also used in a popular 1800 stage production at Drury Lane named 'Harlequin Amulet, or the Majic of Mona,' this in turn resulted in several London publications of the tune being issued under the name 'Harlequin Amulet'. The single most common name for the tune in London, especially after 1802, was 'Cary Owen'."
And note well:
"... [S]everal authorities ascribe the first publication of this tune to a c.1785 London publication issued by Edward Light named 'Introduction to the Art of Playing on the Harp-Lute & Apollo-Lyre.' Light's publication could have included this tune, but as far as I can discern it was first published in 1811 not 1785 (e.g. as advertised in the 'Morning Post' for the 2nd November 1811). The Harp-Lute itself seems not to have been invented until 1795, I'm fairly sure that Light was not significant to the early history of our tune.
The score for 'Harlequin Amulet' might have been printed in London c.1800 (I can't confirm this), but our tune was certainly arranged as a Rondo in Dublin and printed by Hime a year or two later under the name 'Gary Owen'. The first London publication I can actually confirm is that of William Campbell in his 1801 16th Book under the name 'Garey Owen' (see Figure 7, bottom). Campbell described the tune as 'Harlequin Amulet or the Majic of Mona, by Jackson of Cork'."
Notley seems not to mention the title "Garryowen," nor that it may have been the original form of "The Garyon" rather than the other way round.
Allegedly "Garyon" is a surname originating in Connaught, but I' suspicious: I find only one online source that asserts this.
FWIW, Notley's conclusion that Light's book on the harp-lute wasn't published till 1811 is supported by its absence from the enormous "Eighteenth-Century Collections Online" (available through many libraries).