[ http://www.lorcanmacmathuna.com and http://songsinirish.com/p/eleanor-a-run-lyrics.html - translation there is very erroneous ]

Mo ghrá den chéad fhéacaint thú,
Eileanóir a rún.
Is ortsa a bhímse ag smaoíneamh,
Tráth a bhím i mo shuain.
Mo ghrá den tsaol thú,
ó mo chéad searc,
is tú is deise ná ban Éireann,
'S a bhruinnillín deas óg,
is tú is deise, is milse póg,
Ach chúns a mhairfeadsa beo,
beidh gean a'm ort,
Mar is deas mar a sheolfainn
na gamhna leat,
'Eleanóir, a rún.

Bhí bua aici go mealfadh sí
na h-éanlaithe ón gcrann.
Bhí bua eile aici go dtógfadh sí
an suan-choirp ón mbás. // an corp fuair ón mbás
Bhí bua eile aici nach ndeirfeadh mé,mar
sí grá mo chroí is mo chéad searc.
A bhruinillín deas óg, is tú is deise milse póg,
Ach chúns a mhairfeadsa beo, beidh geann am ort.
Mar is deas mar a sheolfainn gamhna leat
Eileanóir a rún.

An dtiocfaidh tú nó a bhfanfaidh tú
Eileanóir a rún
Nó an aithneofá an té nach gcáinfeadh thú,
mo chuid den tsaoil is a stór.
Ó tiocfaidh mé, is ní fhanfaidh mé
Is maith d'aithneoin an té nach gcáinfeadh mé.
A bhruinillín deas óg, is tú is deise milse póg,
chúns a mhairfeadsa beo beidh geann agam ort.
Mar is deas mar a sheolfainn gamhna leat
Eileanóir a rún.

------
by the way, the Joe Einniú version has the words "na rún" and is translated as Eleanor of the secret/s
but usually we have "a rún", the "a" in this case indicating that someone is being addressed, and I wouldn't translate "rún" as secret in this case but as "dear" or "beloved" - [my] intended one
Similar to the the expression "tá rún ag.." (Tá rún agam an t-amhrán seo a fhoghlaim" = "I intend to learn this song"), though it could also imply a secret love.