How about Palestrina's "Sicut cervus"? First line, Sicut cervus desiderat ad fontes aquarum... This text is used in the 1962 Missal Holy Saturday vigil for the procession to the baptismal font after the water is blessed.

The official rite recommends the following. I append the official English translation. I provided this list in Latin and English because I hope that others on this site will know of motets and anthems on these texts.

V. ACCLAMATIONES, HYMNI ET TROPARIA

Acclamationes e libris sacris desumptae

225. Quis símilis tui in fórtibus, Dómine?
Quis símilis tui, magníficus in sanctitáte,
terríbilis atque laudábilis, fáciens mirabília? (Ex 15, 11).

226. Deus lux est, et tenébræ in eo non sunt ullæ (1 Io 1 1, 5).

227. Deus cáritas est,
et qui manet in caritáte in Deo manet (1 Io 4, 16).

228. Unus Deus et Pater ómnium,
qui est super omnes et per ómnia
et in ómnibus nobis (Eph 4, 6).

229. Respícite ad eum et illuminámini (Ps 33, 6).

230. Benedíctus Deus,
qui elegit vos in Christo (cf. Eph 1, 3–4).

231. Dei factúra estis, creáti in Christo Iesu (Eph 2, 10).

232. Caríssimi, nunc fílii Dei estis,
et nondum manifestátum est quid éritis (1 Io 3, 2).

233. Qualem caritatem dedit vobis Pater,
ut filii Dei nominemini et sitis (1 Io 3, 1).

234. Beáti qui lavant stolas suas
in sanguine Agni (Ap 22, 14).

235. Omnes vos unum estis in Christo Iesu (Gal 3, 28 ).

236. ·Estóte imitatóres Dei et ambuláte in dilectióne;
sicut et Christus diléxit nos (Eph 5, 1–2).


Hymni in stylo Novi Testamenti

237. Benedíctus Deus et Pater Dómini nostri Iesu Christi,
qui secúndum magnam misericórdiam suam
regenerávit nos in spem vivam,
per resurrectiónem Iesu Christi ex mórtuis,
in hereditátem incorruptíbilem,
conservátam in cælis propter vos
in salútem témpore novíssimo revelándam (1 Pt 1, 3–5).

238. Magnum est pietátis sacraméntum,
ante mundi constitutiónem præcógnitum,
novíssimis tempóribus manifestátum:
Christus Iesus,
carne passus et mortificátus,
spíritu vivificátus,
géntibus prædic átus,
in mundo créditus,
in cælum proféctus,
dona lárgiens homínibus,
in glória super omnes cælos assúmptus,
ut impléret omnia, allelúia (Cf. 1 Tim 3, 16).


Troparia ex antiquitate et litugiis selecta

239. In te crédimus, Christe:
tuum córdibus lumen infúnde, ut lucis fílii efficiámur.

240. Ad te vénimus, Dómine:
tuam ánimis vitam largíre, ut adoptiónis fílii in te evadámus.

241. E látere tuo, Christe, fons aquæ prorúpit,
quo abluúntur mundi sordes et vita renovátur.

242. Super aquas Patris vox ádvocat, glória Fílii refúlget,
et Spíritus sancti cáritas vivíficat.

243. Ecclésia sancta, manus exténde et natos illos súscipe,
quos ex aquis regénerat Sanctus Dei Spíritus.

244. Gaudéte, baptizáti,
elécta vasa Regni,
in morte consepúlti,
Christi fide renáti.

245. Fons hic est vitæ, qui totum déluit orbem,
sumens de Christi vúlnere princ ípium.
Cælórum Regnum speráte, hoc fonte renáti.

===================

ACCLAMATIONS FROM SACRED SCRIPTURE

225. Exodus 15:11
Lord God, who is your equal?
Strong, majestic, and holy!
Worthy of praise, worker of wonders!

226. 1 John 1:5
God is light: in him there is no darkness.

227. 1 John 4:16
God is love: he who lives in love, lives in God.

228. Ephesians 4:6
There is one God, one Father of all:
he is over all, and through all:
he lives in all of us.

229. Psalm 34:6
Come to him and receive his light!

230. see Ephesians 1:4
Blessed be God who chose you in Christ.

231. Ephesians 2:10
You are God’s work of art,
created in Christ Jesus.

232. 1 John 3:2
You are now God’s children, my dearest friends.
What you shall be in his glory has not yet been revealed.

233. 1 John 3:1
Think of how God loves you!
He calls you his own children,
and that is what you are.

234. Revelation 22:14
Happy are those who have washed their robes clean:
washed in the blood of the Lamb!

235. Galatians 3:28
All of you are one:
united in Christ Jesus.

236. Ephesians 5:1–2
Imitate God, walk in his love,
just as Christ loves us.

HYMNS IN THE STYLE OF THE NEW TESTAMENT
237. 1 Peter 1:3–5
Praised be the Father of our Lord Jesus Christ:
a God so merciful and kind!
He has given us a new birth, a living hope,
by raising Jesus his Son from death.
Salvation is our undying inheritance,
preserved for us in heaven,
salvation at the end of time.

238.
How great the sign of God’s love for us,
Jesus Christ our Lord:
promised before all time began,
revealed in these last days.
He lived and suffered and died for us,
but the Spirit raised him to life.
People everywhere have heard his message
and placed their faith in him.
What wonderful blessings he gives his people:
living in the Father’s glory,
he fills all creation
and guides it to perfection.

SONGS FROM ANCIENT LITURGIES
239.
We believe in you, Lord Jesus Christ.
Fill our hearts with your radiance,
and make us the children of light!

240.
We come to you, Lord Jesus.
Fill us with your life,
make us children of the Father,
and one in you.

241.
Lord Jesus, from your wounded side
flowed streams of cleansing water:
the world was washed of all its sin,
all life made new again!

242.
The Father’s voice calls us above the waters,
the glory of the Son shines on us,
the love of the Spirit fills us with life.

243.
Holy Church of God, stretch out your hand
and welcome your children
newborn of water
and of the Spirit of God.

244.
Rejoice, you newly baptized,
chosen members of the kingdom.
Buried with Christ in death,
you are reborn in him by faith.

245.
This is the fountain of life,
water made holy by the suffering of Christ,
washing all the world.
You who are washed in this water
have hope of heaven’s kingdom.

Michael, was your son baptised in the new or classical form? I ask because it turns out that latter does not allow for singing at all.

Michael,

I'm a computer idiot, and I'm getting some weird notation when I try to download this . . . are you able to make this available in a PDF file?

I was surprised too. This must be an example of the old rite not always being representative of tradition in its best form. I bet there was singing in the old baptisteries of Europe.