Taken from Muwasala: Click here for original blog
When the month of Rajab enters, the Beloved ﷺ would seek its blessings, saying,“O Allah bless us in Rajab and Sha`bān and enable us to reach Ramaḍān!” (Aḥmad, al-Baiḥaqi, Ibn Majah)

[Recommended supplications during the blessed month]

Sayyidī al-Ḥabīb `Umar bin Ḥafīẓ (may Allāh preserve him and benefit us by him) recommends reading the following formulas of istighfār in the blessed month of Rajab.

I seek the forgiveness of Allah for everything that He knows; I seek Allah’s forgiveness in the way that He loves.

أَسْتَغْفِرُ اللهَ ذا الجَلالِ و الإِكْرَام مِنْ جَميعِ الذُّنوبِ و الآثام

Astaghfirullāh dha’l-Jalāli w’al-Ikrām min jamī` adhunūbi wa al-āthām.

I seek the forgiveness of Allah, the Possessor of Majesty and Honour, for all my sins and wrongdoings.

أَسْتَغْفِرُ اللهَ الَّذِي لا إِلَهَ إِلاّ هُوَ الرَّحْمَنَ الرَّحِيمَ الْحَيَّ الْقَيُّومَ الَّذِي لا يَمُوتُ وَأَتُوبُ إِلَيْه رَبِّ اغْفِرْ لِي

Astaghfirullāh alladhī lā ilāha illā huwa arraḥmān arraḥīm al-Ḥayya al-Qayyum alladhī lā yamūtu wa atūbu ilayhi rabbi-ghfir lī

I seek the forgiveness of Allah, besides Who there is no god; the Most Compassionate, the Most Merciful, the Living, the Sustainer, the One Who never dies and I repent to Him. O Lord, forgive me.

[What is being read in Tarim?]

In Tarim the following formula is read 70 times in congregation immediately after the `Ishā’ Prayer every night in Rajab. The one reading it raises his hands while doing so:

رَبِّ اغْفِرْ لي وارْحَمْنِي وَتُبْ عَلَيَّ

Rabbi ‘ghfir lī w’ arḥamnī wa tub `alayya.

O Allāh forgive me, have mercy upon me, and grant me repentance.

It is also good to read what is known in Ḥaḍramawt as Istighfār Rajab, a compilation of istighfār compiled by Ḥabīb Ḥasan, the son of Imām `Abdullāh bin `Alawī al-Ḥaddād:

In the Name of Allāh, the Most Compassionate, the Most Merciful.All praise is due to Allāh Lord of the Worlds.

O Allāh bestow prayers and peace upon our Master Muḥammad and upon his Family and Companions.

I seek the forgiveness of Allāh (3 times) for every word, act and thought and every inward and outward action of mine which Allāh dislikes.

I seek the forgiveness of Allāh, besides Who there is no god; the Living, the Sustainer, and I repent to Him.

O Allāh forgive me for what I have done previously, what I will do, what I have done in secret and in private, for my excesses and for that about which You have more knowledge than I. You are the one who puts people ahead and puts people behind and You have power over all things.

I seek the forgiveness of Allāh, the Possessor of Majesty and Honour, for all my sins and wrongdoings. I seek the forgiveness of Allāh for every one of my sins: those committed in private, those committed in public, the small and the large, those committed previously and those committed recently, the first and the last of them, outward and inward sins, and I repent to Him.

O Allāh I seek Your forgiveness for any sin from which I have repented and then committed again.

I seek Your forgiveness for any action which I performed initially for Your noble countenance and then something else which is displeasing to You detracted from my sincerity.

I seek Your forgiveness for anything that I have promised to do for Your sake and then broken my promise to You.

I seek Your forgiveness for anything that my caprice has called me to do by taking dispensations in affairs which are dubious, which are in Your sight forbidden.

I seek Your forgiveness, there is no god but You, O Knower of the Seen and Unseen, for every wrong or act of disobedience that I have committed in broad daylight or in the darkness of the night, in the company of people or whilst alone, in public or in private, in the knowledge that You were gazing upon me as I committed it. I repent to You, O Forbearing One, O Most Generous, O Most Merciful.

I seek Your forgiveness for deriving strength from the blessings You have bestowed upon me and then using that strength to disobey You.

I seek Your forgiveness for sins which only You know about and only You can see, sins which only Your forbearance can encompass and from which only Your pardon can save me.

I seek Your forgiveness for every oath I have made and then broken, for which I will be taken to account.

I seek Your forgiveness, there is no god but You, transcendent are You, truly I am amongst the wrongdoers. So We responded to him and delivered him from distress; thus do We deliver those who have faith. And remember Zakariyyā, when he cried to his Lord: “O my Lord! Leave me not without offspring, for You are the best of bestowers.”

“My Lord! Forgive and have mercy, for You are the Best of those who show mercy.”

I seek Your forgiveness for every obligation which You have requested that I fulfil in the day or the night which I have subsequently neglected out of heedlessness, absent-mindedness, forgetfulness or ignorance, and for which I will be punished.

I seek Your forgiveness for every sunnah of the Master of the Messengers, the Seal of the Prophets, Your Prophet our Master Muḥammad (peace and blessings upon him) which I have left out of heedlessness, absent-mindedness, forgetfulness, ignorance or not caring.

I seek Your forgiveness, there is no god but You, alone without partner, Muhammad is Your slave and messenger. Transcendent are You, O Lord of the Worlds. To You belongs the dominion and all praise. You are sufficient for us, and You are the best disposer of our affairs. He is the best of those who protect and the best of those who assist. There is no strength nor might except in Allāh, the Sublime, the Awesome.

O Allāh, You are the Repairer of every breakage, the Companion of everyone who is alone, the One who brings ease to every difficulty, the One who is not in need of clarification or explanation. You are able to do whatever You will.

Send blessings upon our Master Muḥammad to the number of those who send blessings upon him, and to the number of those who do not. O Allah send blessings upon the spirit of our Master Muḥammad, upon the earth in which our Master Muḥammad is buried, upon the grave in which our Master Muḥammad lies, upon the physical form of our Master Muḥammad and upon the name of our Master Muḥammad.

There has come to you a Messenger from among yourselves, grievous to whom is your burden, concerned (is he) for you; for the believers (he is) full of compassion, merciful. If they turn away then say: Allāh is sufficient for me; there is no god but He. On Him do I rely; He is the Lord of the Awesome Throne.

May peace and blessings of Allāh be upon our Master Muḥammad and upon his Family and Companions. All praise is due to Allāh, Lord of the Worlds, in every instant forever, the number of His creation, to His satisfaction, the weight of His throne and the amount of ink of His words.

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Useful resources

Watch this beautiful lesson on Rajab by Habib Khadhim translated by Shaykh Ibrahim Osi Efa
http://youtu.be/oxy62lB8I4o