I can do a rough translation of the verse Keberoxu posted

Hups, a Sheáin, a bhráthair, fuair do mháthair bás
Ó, ní bhfuair, ní bhfuair do chuaigh sí suas an tsráid

hup, Seán, o brother, your mother has died
oh no she hasn't, she went up the street
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There are a few similar sets of lyrics and tunes (not exactly the same, but close) in Irish

Caithfimid suas is suas í (We will throw her up and up)
Caithfimid suas go heasc í (We will throw her up easily)
Caithfimid suas is suas Í (We will throw her up and up)
I seacain a chroí na pleasc í (Hopefully she will not explode)

Caithfimid suas is suas í (We will throw her up and up)
Caithfimid suas go heasc í (We will throw her up easily)
Caithfimid suas is suas í (We will throw her up and up)
I seacain a chroí na pleasc í (Hopefully she will not explode)

Curfá: Chorus (after each verse):
Déanfaidh sí damhsa is damhsa (She will dance and dance)
Déanfaidh sí damhsa le pléisiúr (She will dance with pleasure)
Déanfaidh sí damhsa is damhsa (She will dance and dance)
Mé féin is í féin le chéile (Myself and her together)

Déanfaidh sí damhsa is damhsa (She will dance and dance)
Déanfaidh sí damhsa le pléisiúr (She will dance with pleasure)
Déanfaidh sí damhsa is damhsa (She will dance and dance)
Mé féin is í féin le chéile (Myself and her together)

Caithfimid suas is suas í (We will throw her up and up)
Caithfimid suas an páiste (We will throw the child up)
Caithfimid suas is suas í (We will throw her up and up)
Is tiocfaidh sí anuas amárach (And she'll come down tomorrow}

Caithfimid suas is suas í (We will throw her up and up)
Caithfimid suas an páiste (We will throw the child up)
Caithfimid suas is suas í (We will throw her up and up)
Is tiocfaidh sí anuas amárach (And she'll come down tomorrow)

Caithfimid suas is suas í (We will throw her up and up)
Caithfimid suas go heasc í (We will throw her up easily)
Caithfimid suas is suas í (We will throw her up and up)
I seacain a chroí na pleasc í (Hopefully she will not explode)

Caithfimid suas is suas í (We will throw her up and up)
Caithfimid suas an páiste (We will throw the child up)
Caithfimid suas is suas í (We will throw her up and up)
I seacain a chroí na pleasc í (Hopefully she will not explode)

[The singer is bouncing the baby on his/her lap, not "throwing" her. If the baby is a boy, sing "é" rather than "í" at the end of each line]

above lyrics taken from www.elyrics.net

-------------------------
DEANDAÍ DEANDAÍ

Cuirfimid deaindí, deaindí
Cuirfimid deaindí ar Mháire
Cuirfimid deaindí, deaindí
Bróga is stocaí bána

CHORUS:

Hóró damhas is damhas
Is hóró damhas go haerach
Hóró damhas is damhas
Is damhas is damhas a lao dhil

Rachaidh mé siar is siar
Rachaidh mé siar lem stoirín
Rachaidh mé siar is siar
Is fanfaimid thiar ag spórtaíocht

Caithfimid suas is suas é
Caithfimid suas an páiste
Caithfimid suas is suas
Is tiocfa’ sé ‘nuas amárach

SUMMARY TRANSLATION

We will dancle Máire, white shoes and socks

dance and dance, dance airily, my dear one (literally lao =calf)

I will go west with my little treasure, and we will stay and sport and play

I will toss him up and he'll come down tomorrow
------------------
DILÍN Ó DEAMHAS

Dilín ó deamhas ó deamhas
Dilín ó deamhas ó dí
Dilín ó deamhas ó deamhas ó deamhas ó
Dilín ó deamhas ó dí

Chuiread* mo rún chun suain,
Chuiread mo rún 'na luí,
Chuiread mo rún chun suain go ciúin,
Le dilín ó deamhas ó dí.

(Curfá/chorus)

Is buachaill aniar aniar,
Is buachaill aniar an fear,
Is buachaill aniar aniar aniar,
'S is cailín ón sliabh a bhean.

(Curfá)

Caithimis suas is suas é,
Caithimis suas an páiste,
Caithimis suas is suas is suas é,
'S tiocfaidh sé 'nuas amárach

translation

Dilín ó deamhas ó deamhas
Dilín ó deamhas ó dí
Dilín ó deamhas ó deamhas ó deamhas ó
Dilín ó deamhas ó dí.

I lulled my darling to sleep
I put my darling to bed
I lulled my darling to sleep to sleep,
With dilín o deamhas o dí.

(Chorus)

The boy is from the West, the West,
The boy is from the West, a man,
The boy is from the West, West, West,
And the girl from the mountain his lady.

(Chorus)

Toss him upwards and up,
Toss the child up,
Toss him upwards and up and up,
And he'll come back tomorrow