It is reported that when Hazrat Abdullah bin Umar and Hazrat Abdullah bin Abbas would make Istilaam of the Hajar-e-Aswad, they would recite the following Dua:
اَللَّهُمَّ إِِيْمَانًا بِكَ وَتَصْدِيْقًا بِكِتَابِكَ وَسُنَّةِ نَبِيِّكَ
“O Allah (I am carrying out this action of Istilaam) due to having Imaan in You, and believing in the truthfulness of Your kitaab and (following) the Sunnah of Your Nabi صلى الله عليه وسلم!”
After reciting the abovementioned dua, Hazrat Ibnu Umar رضى الله عنهما would recite Durood Shareef. (Mujamul Awsat #5486)
(Hajj- the Fifth Pillar of Islam pg.116)