You will be permitted to supplicate

A: Parents have a great right that follows the Right of Allah (Exalted be He) as indicated by His Saying, Worship Allâh and join none with Him (in worship); and do good to parents This is to be done by showing kindness and compassion to them in word and action and avoiding abusing them by words or deeds. Allah Almighty says, ...say not to them a word of disrespect, nor shout at them but address them in terms of honour. And lower unto them the wing of submission and humility through mercy, and say: "My Lord! Bestow on them Your Mercy as they did bring me up when I was young." (Part No. 24; Page No. 223) However, there is no specific Du`a' with regard to parents except for saying "My Lord! Bestow on them Your Mercy," and "My Lord! Forgive me and my parents," and the like that includes nothing objectionable. As for what is mentioned in the other Du`a', it has no reference. The Prophet (peace be upon him) said, Whoever does any act for which there is no sanction from our behalf will have it rejected. This covers specifying a Du`a' without evidence. Moreover, This Du`a' contains exotic phrases such as "O Allah! Forgive their negligence of Your Rights on account on their preoccupation with bringing us up," and "Forgive them on account of the services they provided for you," which is a Sufi phrase, for Allah is never in need of service; rather it is His Right to be worshipped. Therefore, it is not permissible to print or propagate this Du`a'. It is sufficient to make use of the Du`a's reported in the Book and Sunnah.May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.