Sayyid Abdullah bin Muhammad bin Ahmad Mashhur al-Haddad narrates that his grandfather, Habib Ahmad Mashhur al-Haddad (may Allah have mercy upon him and benefit us by him), gave permission for the following to be recited in order to see the Prophet ﷺ.
Recite this verse of the Burdah of Imam al-Busiri followed by any prayer upon the Prophet ﷺ. Repeat this ten times:
نَعَمْ سَرَى طَيْفُ مَنْ أَهْوَى فَأَرَّقَني
وَ الْحُبُّ يَعْتَرِضُ اللَّذَّاتِ باِلأَلَمِ
Na`am sara tayfu man ahwa fa arraqani
Wa’l-hubbu ya`taridu’l-ladhdhati bi’l-alami
Yes, a vision of the one I love came to me by night, and I could not sleep,
Oh, how love hinders the tasting of delight with its suffering
A second method Habib Ahmad mentioned was to go bed on Thursday night in a state of complete purity and to recite the same verse of the Burdah once followed by this prayer upon the Prophet ﷺ seven times:
اللَّهُمَّ صَلِّ على سَيِّدِنا مُحَمَّدٍ حَبِيبِ الرَّحْمَن وسَيِّدِ الأكْوَان الحاضِر مَعَ مَنْ صَلَّى عَلَيْهِ في كُلِّ زَمَان ومَكان
Allahumma salli `ala sayyidina Muhammadin habibirrahman wa sayyidi’l-akwan al-hadir ma` man salla `alayhi fī kulli zaman wa makan
O Allah, bestow Your blessings upon our Master Muhammad, the Beloved of the All Merciful, the master of all creation, the one who is present with whoever bestows prayers upon him in every time and place.