We do not know of any du‘aa’s in the saheeh Sunnah that are specifically for the pregnant woman or the baby. Whatever has been narrated concerning that is either fabricated or has been compiled by some scholars from verses and du‘aa’s that are suited to the occasion, without attributing any of that to Islamic teachings per se.
1. Example of a fabricated report
There is a report which says that when the time of birth drew near for Faatimah (may Allah be pleased with her), the Messenger of Allah (blessings and peace of Allah be upon him) instructed Umm Salamah and Zaynab bint Jahsh to come and recite beside her Aayat al-Kursi and the verse “Indeed your Lord is Allah, Who created the heavens and the earth…” [al-A‘raaf 7:54, Yoonus 10:3], and to recite al-Mu‘awwidhatayn (the last two soorahs). But this is a fabricated hadeeth. See: al-Kalim at-Tayyib (p. 161) by Ibn Taymiyah, annotated by al-Albaani.
2. Example of ijtihaad
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) was asked: Are there any verses that may be recited for the purpose of making childbirth easier for the woman?
I do not know of anything of that nature in the Sunnah, but if you recite over the pregnant woman who is in labour that which speaks of things being made easier, such as the verse (interpretation of the meaning): “Allaah intends for you ease, and He does not want to make things difficult for you”[al-Baqarah 2:185]; and that which speaks of childbirth and delivery, such as the verse (interpretation of the meaning): “And no female conceives or gives birth, but with His Knowledge” [Faatir 35:11] – this will be beneficial; it has been tried and tested, by Allah’s leave. The entire Qur’an is healing; if the reciter and the one to whom it is recited believe in its impact then it must inevitably have an effect, because Allah, may He be glorified and exalted, says (interpretation of the meaning): “And We send down from the Qur’an that which is a healing and a mercy to those who believe (in Islamic Monotheism and act on it), and it increases the Zalimoon (polytheists and wrong-doers) nothing but loss” [al-Isra’ 17:82]. This verse is general in meaning; healing and mercy includes healing of hearts from the diseases of doubt and desire, as well as the healing of bodies from physical disease. End quote.
Fataawa Noor ‘ala ad-Darb, tape no. 257, side A.
The prayer of a mother for her child is answered, so there is the hope that the prayer of the pregnant woman for her baby will be accepted by Allah, may He be exalted, if she fulfills the conditions of supplication and avoids any impediments to it receiving a response.
She should offer a great deal of supplication, asking for the baby’s well being and that he be righteous, guided and enabled to do good, and that he will honour his parents.
And Allah knows best.