Are there any verses which pray for the birth of daughter in Vedas?
It is not that the Vedas only praise the birth of a male child alone. There are instances where female progeny is also praised. Further, it is important to know that the word "putra" does not necessarily mean only male child but could mean child in general. Similarly in many places word "man" does not only indicate men but all of the mankind including men and women.
O Brahman, let there be born in the kingdom the Brahman illustrious for religious knowledge; let there be born the Râjanya, heroic, skilled archer, piercing with shafts, mighty warrior; the cow giving abundant milk; the ox good at carrying; the swift courser; the industrious woman. May Parjanya send rain according to our desire; may our fruit-bearing plants ripen; may acquisition and preservation of property be secured to us. (Shukla Yajurveda 22.22)
My Sons are slayers of the foe, my Daughter is a ruling Queen: I am victorious: o’er my Lord my song of triumph is supreme. Rigveda 10.159.3
With sons and daughters by their side they reach their full extent of life, Both decked with ornaments of gold. R.V 8.31.8
With many a son, father of many daughters, He clangs and clashes as he goes to battle. Slung on the back, pouring his brood, the Quiver vanquishes all opposing bands and armies. R.V 6.75.5
Some scholars have attempted to prove the daughter as an unwelcome member of the family but it’s absolutely against the tenets of the Vedas which suggest quite the opposite to these claims. In subsequent ages women have been denied the privilege of Upanayana too which is not in accordance with the vedic injunctions. See the following quotes from the gRhya sUtras: (Which are the practical manuals for conducting the Vedic rites and rituals)
Parents desirous of obtaining a daughter perform the KAmya ShrAddha on the second day of the moon (Gobhila ParishiSTa ShrAddha Kalpa [Calcutta ed.p.186] ## PAraskara GRhya Sutra 1.21 )
When a husband is desirous of having a daughter, he should touch all the fingers of his wife except her thumb during the marriage ceremony. (AshvalAyana GRhya SUtra 2:125, Apastamba GRhya SUtra यदि कामयेत स्त्रीरेव जनयेयमित्यङ्गुलिरेव गृह्णीयात् 6:12)
Wishing for a daughter, the husband shows the bride the Dhruva and other constellations ( kAthaka Grhya Sutra commentary जीवन्तीं कन्यामिच्छन् ध्रुवादिकं दर्शयेत् 2 :1-2 )
So it is very obvious to a discerning person that the girl child was never disliked or unwelcome in the household. In fact special prayers and propitiations were conducted to have a girl in the family!
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