Is there a specific Du'a to say to live peacefully with one's wife and to have good religious children?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

If the inquirer means a special Du'aa’ (supplication) after establishing wedlock, we say that there is no such Du'aa’ except Allah's Statement describing His pious Slaves in Chapter Al-Furqaan (which means): {And those who say, "Our Lord, grant us from among our wives and offspring comfort to our eyes and make us an example for the righteous."} [Quran 25: 74]
Ibn 'Abbas said: “This verse indicates that those who obey Allah, He will make their wives as consolation to them in this worldly life and in the Hereafter.”

Ibn Jurayj said that the offspring in the same verse means: “Children who will worship Allah in the way He wants and will not cause us any shame.”

So, a Muslim is advised to repeat such a verse (since it is a comprehensive Du'aa’).

Here are some other forms of comprehensive and sound supplications:

• “O Allah! Set right all my affairs and give me not over to myself nor to anybody from among Your Creation.”

• “O Allah! Send Your blessings upon my family and property.”

• The Prophet Zakariyah's Du'aa’: {“…My Lord, grant me from Yourself a good offspring. Indeed, You are the Hearer of supplication.”} [Quran 3: 38]

Allah knows best.