Reference : Hisn al-Muslim 145

(بَارَكَ اللَّهُ لَكَ فِي الْمَوْهُوبِ لَكَ، 
وَشَكَرْتَ الْوَاهِبَ، 
وَبَلَغَ أَشُدَّهُ، 
وَرُزِقْتَ بِرَّهُ).
 
 وَيَرُدُّ عَلَيْهِ الْمُهَــــــنَّأُ فَيَقُولُ:
(بَارَكَ اللَّهُ لَكَ وَبَارَكَ عَلَيْكَ، 
وَجَزَاكَ اللَّهُ خَيْراً، 
وَرَزَقَكَ اللَّهُ مِثْلَهُ، 
وَأَجْزَلَ ثَوَابَكَ).
Bārakallāhu laka fi ‘l-mawhūbi lak, 
wa shakarta ‘l-wāhib, 
wa balagha ashuddah, 
wa ruziqta birrah.

The reply of the person being congratulated is to say:

Bārakallahu laka wa bāraka `alayk, 
wa jazākallāhu khayra, 
wa razaqakallāhu mithlah, 
wa ajzala thawābak.


May Allah bless you with His gift to you, 
and may you (the new parent) give thanks,
may the child reach the maturity of years,
and may you be granted its righteousness. 

The reply of the person being congratulated is to say:

May Allah bless you, and shower His blessings upon you, 
and may Allah reward you well
and bestow upon you its like 
and reward you abundantly

Reference:
An-Nawawi, Kitdbul-'Athkarp. 349, and Sahihul-'Athkar2/7l3 by Saleem 
Al-Hilali.

Chapter: Congratulation on the occasion of a birth and its reply