There is no specific dhikr to be said in the two prostrations of forgetfulness as far as we know. Based on this, they come under the same ruling as prostration in prayer, and the same should be said as in the prostration in prayer, such as “Subhaan Rabbiy al-a’la (Glory be to my Lord Most High) and du’aa’, because the Prophet (peace and blessings of Allaah be upon him) said: “The closest a person can be to his Lord is when he is prostrating, so say a great deal of du’aa’ (at that time).” Narrated by Muslim, 482.
The same should be said between the two prostrations as is said between the two prostrations in prayer, namely “Rabbiy ighfir li (Lord forgive me).
See question no. 13340.
Al-Nawawi said in al-Majmoo’ (4/72):
The prostration of forgetfulness is two prostrations, sitting in between them. It is Sunnah to sit muftarishan (with the left foot lying along the ground and sitting on it) in between them, and to sit mutawarrikan (with the left upper thigh on the ground and both feet protruding from one (i.e., the right) side) after them until one says the salaam. The way in which the prostrations are done and the dhikr to be said in them is the same as in the prayer. And Allaah knows best. End quote.
It says in al-Sharh al-Kabeer (4/96):
He should say in the prostration of forgetfulness the same as he says in the prostration of prayer, by analogy with it. End quote.
It says in Asna al-Mataalib (1/195):
The prostration of forgetfulness is two prostrations… the way in which they are done is the same as in prayer. He should sit muftarishan between them, and recite the same dhikr as in the prostration during the prayer. End quote.
It says in Mughni al-Muhtaaj (1/439):
The way in which it is done is the same as in prayer, both obligatory and naafil prayers, such as putting the forehead on the ground and being at ease (in the posture)… and he should say the same dhikr as in the prostration of prayer.
Al-Adhra’i said: And they did not say anything about the dhikr to be said in between them. It seems that it is the same as the dhikr between the two prostrations of the prayer. End quote.
It says in Fataawa al-Lajnah al-Daa’imah (6/443):
When doing the prostration of forgetfulness and prostrations required when reading Qur’aan, he should say the same as he says when prostrating during the prayer: “Subhaan Rabbiy al-a’la (Glory be to my Lord Most High)”. What is required is to say it once, but the least level of perfection is to say it three times. It is mustahabb to say du’aa’ whilst prostrating, saying whatever du’aa’s prescribed in sharee’ah one can. End quote.
Some of the scholars stated that it is mustahabb to say in these prostrations: “Subhaana man laa yanaamu wa la yas-hu (Glory be to the One Who does not sleep or forget).”
Al-Haafiz ibn Hajar said in al-Talkhees (2/12): I could not find any basis for this.” End quote.