All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Scholars of Islam differ concerning the Prayer for need due to their difference about the authenticity of the Hadeeth narrated in this concern. However, it is permissible to act according to the Hadeeth that describes the Prayer for need because of (1) its several narrations that strengthen one another; (2) it is permissible to act according to a weak Hadeeth in meritorious deeds; (3) it is not very weak and comes under general principles of the Sharee'ah; and (4) it does not contradict a sound Hadeeth.
Know, that there is not a specific way nor portions of the Quran that are advised to be recited in the Prayer for need.
But a person can perform a prayer of two Raka'hs, and then supplicate to Allah with the following supplication:
“None has the right to be worshipped except Allah the Forbearing. Glory be to Allah, The Lord of the Universe. O Allah! I ask you to bestow Your Mercy on me, to forgive me, to protect me from every sin, to give me a share of every good and to grant me safety from crime (sin). Leave no sin of mine but You pardon it nor sorrow but you dispel it. O Allah! I ask You to satisfy my every need that is desirable to You. O The Most Merciful One.”
For more benefit on Salaatul-Haajah (Prayer of need), please refer to Fatwa 82384.
Allah knows best.