Praise be to Allah.
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 Subhan Rabbiy Al-a’la (Glory be to my Lord Most High) and Du`a, because the Prophet (peace and blessings of Allah 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`a (at that time).” (Narrated by Muslim, 482)
Al-Nawawi said in Al-Majmu’ (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 Salam. The way in which the prostrations are done and the Dhikr to be said in them is the same as in the prayer. And Allah knows best.”
It says in Al-Sharh Al-Kabir (4/96):
“He should say in the prostration of forgetfulness the same as he says in the prostration of prayer, by analogy with it.”
It says in Asna Al-Matalib (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.”
It says in Mughni Al-Muhtaj (1/439):
“The way in which it is done is the same as in prayer, both obligatory and Nafl (supererogatory) 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-Athra`i said: “And they (scholars) 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.”
It says in Fatawa Al-Lajnah Al-Da’imah (6/443):
“When doing the prostration of forgetfulness and the prostrations required when reading the Quran, he should say the same as he says when prostrating during the prayer: “Subhan 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 commendable to say Du`a whilst prostrating, saying whatever Du`as prescribed in Shari`ah one can say.”
Some of the scholars stated that it is commendable to say in these prostrations: “Subhana man la yanamu wa la yas-hu (Glory be to the One Who does not sleep or forget).”
However, Ibn Hajar said in Al-Talkhis (2/12): “I could not find any basis for this.”
And Allah knows best.