When making istilaam of the Hajar-e-Aswad, one should recite the following dua:
بِسْمِ اللهِ وَاللهُ أَكْبَرُ
(I commence the tawaaf) in the name of Allah, and Allah is the greatest!
عن نافع: أن ابن عمر كان إذا استلم الركن قال: بسم الله والله أكبر (مصنف عبد الرزاق، الرقم: 8894)
Hazrat Naafi (rahimahullah) reports that when Hazrat Abdullah bin Umar (radhiyallahu anhuma) would make istilaam of the Hajar-e-Aswad, he would recite the following dua:
بِسْمِ اللهِ وَاللهُ أَكْبَرُ