Here are both tunes for comparison.

X:1
T:Down by Blackwaterside
S:Winnie Ryan, Belfast, 1952
N:BBC recording 18551
N:Roud 564, Laws P18
B:Kennedy, Folksongs of Britain and Ireland. No 151 p 351.
L:1/8
Q:1/4=100
M:3/4
K:Bb
D FF|B3 c (3ded|
w:One morn-ing fair, I took_ the
M:4/4
c3 c BB _AG|
w:air Down by Black-wa-ter-
M:3/4
F2 (3zDF (3GFG|B3 D (3EDE|F2-(3FCD (3EDC|B,3 B, HB,|]
w:side O, then, gaz_ing all a-round__ me_ 'Twas an Ir_ish girl I spied.

X:2
T:Blackwater Side
S:Paddy Tunney; previously Paddy Doran (early 1950s).
B:Paddy Tunney, The Stone Fiddle. Dublin: Gilbert Dalton, 1979; 108-9.
N:Roud 564, Laws P18
L:1/8
Q:1/4=100
M:4/4
K:Eb
e d|c2 (de) c2 (BF)|(GF) E2 C2 (EF)|(GB-B) (G/F/) E3 E|
w:Oh as I roved_ out one_ morn_ing fair, down_ by__ Black_wa-ter
E6 E F|(3G2F2G2 B2 (cd)|e3 c d2 e c|d (GG) =A (3B2-c2d2|
w:side, I being gaz_ing all a_round (e) me, when an I-rish_ young girl_ I
c6 c B|(3G2F2G2 B2 c d|(3e2c2d2 e c|d (G-G=A) (3B2c2d2|
w:spied. Oh for red and (e) ros-y it was her cheeks, gol-den yel-low__ was_ her
c6 (ed)|c2 (de) c2 (BF)|(3G2F2E2 C2 E F|B2 G F E3 E|E6|]
w:hair. I_ caught her_ by the_ lil-y white hand and I said: "My young la-dy fair."