I'm refreshing an old request.

Here's the entry from The Fiddler's Companion:

PADDY WILL YOU NOW? AKA and see "Tow Row Row." Irish, March (2/4 time). G Major. Standard. AABB. O'Neill (1922) says: "The above setting differs not materially from that in Clinton's 200 Irish Melodies for Flute, Dublin 1840. Under the same name a much simpler version appears in Haverty's 300 Irish Airs, New York 1858, having but the exceptional number of 13 bars altogether. To the editor this strain was known in boyhood days as 'Tow Row Row' both names being taken from the first line of the song Tow Row Row, Paddy, will you now, which song by the way cannot be found in any Irish collection at present available. 'Ta na la' or 'It is day' one of three tunes of that name in Stanford-Petrie Collection is obviously the same strain. The arrangement however is quite different; the melody and chorus together consisting of but 17 bars. To add to the diversity, we find that the arrangement of 'Paddy will you now' to which is set Gavan Duffy's poem 'Watch and Wait' in Ballads and Songs by the Writers of "The Nation" Dublin 1845 is limited to 14 bars." O'Neill (Waifs and Strays of Gaelic Melody), 1922; No. 51.

X:1
T:Paddy Will You Now
M:2/4
L:1/16
S:Capt. F. O'Neill
Z:Paul Kinder
R:Air
K:G
(3def|g2B2 B2AG|F2A2 A2BA|G2g2 gfga|b2g2 g2(3def|
g2B2 B2AG|F2A2 A2BA|B2g2 gfga|b2g2 g2:|
|:Bc|d2B2 d2ef|g2f2 e2d2|d2B2 d2ef|g2f2 e2d2|
eeee e2d2|g2B2 B2A2|GGGF G2A2|
B2G2 E2D2|GGGF G2B2|AAAB A2B2|B2g2 f2e2|
d2c2 B2A2|GGGG G2B2|AAAA A2B2|B2g2 f2a2|g4 g2:||