According to Aloys Fleischmann, ed., Sources of Irish Traditional Music c. 1600-1855, 2 vols. (New York: Garland, 1998), the earliest record is in E. Light, ed., A Select Collection of Scottish & Irish Airs for the Voice, No. 5, vol. II (1790). The following are from Fleischmann.

X:1
T:Tell Me Dear Eveleen
M:C
L:1/8
S:Light, A Select Collection of Scottish & Irish Airs, 1790
N:Fleischmann no. 2986
K:G
g2 g3/2g/ f2 f3/2f/|egfe ^dBz2|e2 e3/2e/ ^dBzB|e2 f3/2f/ g2zg|
a2 bg f2 gf|egfe ^dBz2|e2 e2 gfe^d|e2~f2 g4||
efga b2z2|c'2 ba b2 e2|e2 e2 c'3 b|{b/}a2 {a/}g2 f4|
{e/}b4 e3 g|fgfe ^d2 B2|e3 e gfe^d|e2 ~f2 g4|]

X:2
T:Arah My Dear Ev'leen
M:2/2
L:1/8
S:Holden, A Collection of Old Established Irish Slow & Quick Tunes, c1805
N:Fleischmann no. 4521
K:C
c2 c3/2c/ B2 B2|AcBA ^G2 E2|A2 A2 A^GEE|A2 B2 c2 z2|
c2 ec B2 cB|AcBA A^GFE|A2 A2 A^GFE|A2 B2 c4| %or ...|AcBA A^G^FE|A2 A2 A^G^FE|...
|:ABcd e2 e2|f2 ed e2 A2|AA A2 f3 e|d2 c2 B4|
e4 A3 c|BcBA A^GFE|A2 AA cBA^G|A2 B2 c2z2:|] %or e4 a3 c|BcBA A^G^FE|...

X:3
T:The Song of Fionnuala
M:C
L:1/8
S:T. Moore, A Selection of Irish Melodies, bk II, c1807
N:Fleischmann no. 4766
K:C
c2 c3/2c/ {c/}B2 BB|Ac BA ^GEz2|A2 A3/2A/ ^GE z E|A2 B3/2B/ {B/}c2zB|
c2 ec {c/}B2 cB|Ac BA ^GEz2|A2 A3/2A/ cB A^G|A2 B2 {B/}c2z2|
AB cd e2 z e|f2 ed eAz2|A2 z A f3 e|{e/}d3 c {c/}B2z2|
e3 A A2zc|Bc BA ^GEz2|A3 A cB A^G|A2 B2 {B/}c2z2|]