There is no specific du’aa’ narrated in the ahaadeeth for sujood al-shukr, hence the scholars said that what is to be said in sujood al-shukr is the same tasbeeh and du’aa’ as are said when prostrating in prayer. So one should say Subhaana Rabbiy al-A’laa (Glory be to my Lord Most High), Allaahumma laka sajadtu wa bika aamantu wa laka aslamtu, sajada wajhi lillahi khalaqahu wa sawwarahu wa shaqqa sam’ahu wa basarahu, tabaaraka Allaah ahsan ul-khaaliqeen (O Allaah, unto You I prostrate, in You I believe and to You I submit. My face has prostrated to the One who created and formed it, and gave it hearing and sight. Blessed be Allaah, the best of creators). Then he should make du’aa’ as he likes. 

Ibn Qudaamah (may Allaah have mercy on him) said: the description, rulings and conditions of sujood al-shukr are the same as those for sujood al-tilaawah (prostration required when reciting certain verses of Qur’aan). (al-Mughni, 2/372). And he said concerning sujood al-tilaawah: he should say in this prostration what he says in the prostration during prayer. (al-Mughni, 2/362). 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: “Sujood al-shukr is done in response to a calamity that is averted or a blessing which come to a person. It is like sujood al-tilaawah outside prayer. Some of the scholars said that wudoo’ and takbeer is required, and some said that only the first takbeer is required. Then he should fall down in prostration, and make du’aa’ after saying “Subhaana Rabbiy al-A’laa (Glory be to my Lord Most High).”

(Fataawa Islamiyyah, 1/205)

 And Allaah knows best. May Allaah send blessings and peace upon our Prophet Muhammad.