Firstly, with regard to the du`a’ said in sujud at-Tilawah (recital prostration), the late prominent scholar Sheikh Ibn Baz, states,

“The same dhikr and du`a’ prescribed in the regular prostration during prayer are to be said in sujud at-Tilawah, according to the purport of the hadiths in this regard. Among these du`a’s is: 

“Allahumma laka sajadtu, wa bika ‘amantu, wa laka aslamtu, sajada wajhi li-lladhi khalaqahu wa sawwarahu, wa shaqqa sam`ahu wa basarahu, bi-hawlihi wa quwwatihi, tabarak Allah ahsan al-khaliqin”

(O Allah, for You I have prostrated and in You I have believed, and to You I have submitted. My face has prostrated before Him Who created it and formed it, and brought forth its faculties of hearing and seeing by His might and power. Blessed is Allah, the Best of creators.) 

This was narrated by Muslim in his Sahih and said that the Prophet (peace and blessings be upon him) used to say this dhikr during the prostration of prayer, according to the hadith of ‘Ali (may Allah be pleased with him).

We have mentioned above that it is prescribed to say the same in sujud at-Tilawah as in the prostration in prayer. It was narrated that the Prophet (peace and blessings be upon him) used to say the following du`a’ when he did sujud at-Tilawah, and he would say:  

Allahumma ‘uktub li biha ‘indaka ajran, wa ‘mhu ‘anni biha wizran, waj`alha li `indaka dhukhran, wa taqabbalha minni kama taqabbaltaha min ‘abdika Dawud”

(O Allah, record for me a reward for this (prostration), and remove from me a sin; save it for me and accept it from me just as You accepted it from Your slave Dawud).” (At-Tirmidhi) 

However, what is obligatory is to say “subhanarabbiyAl-A`la” (Glory be to my Lord Most High), just as it is obligatory during the prostration of prayer. Any additional du`a’ or dhikr is religiously desirable. 

It is worthy to mention here that sujud at-Tilawah, whether during prayer or outside of it, is sunnah not obligatory, as stated in the Hadith of Zayd ibn Thabit and the hadith of ‘Umar (may Allah be pleased with him).

As for the du`a’s said in sujud as-sahw, the following is a fatwa issued by the Standing Committee for Islamic Research and Ifta’, in this concern. It states,  

“When performing sujud as-sahw (prostration of forgetfulness” and prostration required when reciting the Qur’an, one should say the same as one says when prostrating during the prayer: “subhan rabbiy Al-A’la (Glory be to my Lord Most High)”. What is obligatory is to say it once, but the least level of perfection is to say it three times.

It is recommendable to supplicate Allah whilst prostrating, saying whatever du`as prescribed in sharia that one can.”

May Allah guide all to what pleases Him