Is there any saheeh report that says the du‘aa’ of a pregnant woman will be answered?

After researching the matter, we have not found anything to indicate that the du‘aa’ of a pregnant woman will be answered, either in the marfoo‘ hadeeths (those that are attributed to the Prophet (blessings and peace of Allah be upon him)) or in mawqoof reports (those that are attributed to the Sahaabah). 

But if the Muslim combines positive thinking about Allah, may He be exalted, and certainty of His generosity with proper humility before Him, then we hope that Allah will answer his du ‘aa’s and fulfil his hopes. 

It remains for us to note that the du‘aa’ of the mother for her child is one of the du‘aa’s that will be answered, because the Prophet (blessings and peace of Allah be upon him) said: “There are three du‘aa’s that will undoubtedly be answered: the du‘aa’ of one who has been wronged, the du‘aa’ of the traveller and the du‘aa’ of a father  for his child.”

Narrated by at-Tirmidhi (1905). See also Saheeh al-Adab al-Mufrad, 372 

Al-Mannaawi (may Allah have mercy on him) said:  

“The du‘aa’ of the father for his child” is because he is truly compassionate towards him and often prefers him to himself. As his compassion is genuine, then his du‘aa’ will be answered. The mother is not mentioned even though the emphasis on her rights may indicate that her du‘aa’ is more likely to be answered than that of the father, because this is something that is well known. End quote. 

Fayd al-Qadeer, 3/301 

If a pregnant woman prays for her baby to be righteous, smart and of good character, then we hope that Allah will answer her prayer. 

Please see also the answer to question no. 13506 for a discussion on the conditions of du‘aa’ being answered. 

And Allah knows best.