Is it mustahabb to recite a specific du‘aa’ when kissing the Black Stone?
Question

What is the du‘aa’ for kissing the Black Stone?
Praise be to Allah.The Sunnah when touching or kissing the Black Stone when starting tawaaf is to say: 
“Bismillah, wa Allahu akbar (in the name of Allah, and Allah is most great).” If one adds “Allahumma eemaanan bika wa tasdeeqan bi kitaabika wa wafaa’an bi ‘ahdika wa ittibaa‘an li Sunnati Nabiyyika Muhammad sall-Allahu ‘alayhi wa sallam (O Allah, out of faith in You, and in belief in Your Book, and in fulfilment of Your covenant, and following the Sunnah of Your Prophet Muhammad blessings and peace of Allah be upon him)”, there is nothing wrong with that. 
The evidence for that is the report narrated from Ibn ‘Abbaas (may Allah be pleased with him), according to which the Messenger of Allah (blessings and peace of Allah be upon him) circumambulated the Ka‘bah on a camel, and every time he came to the corner [where the Black Stone is], he pointed to it with something in his hand and said takbeer.
Narrated by al-Bukhaari (1632). 
It was narrated by ‘Abd ar-Razzaaq in al-Musannaf (5/33) from Ibn ‘Umar (may Allah be pleased with him) that when he touched the corner [where the Black Stone is] he said: Bismillah, wa Allahu akbar (in the name of Allah, and Allah is most great).
Classed as saheeh by al-Haafiz Ibn Hajar in at-Talkhees al-Habeer (2/247). 
It was narrated from Ibn ‘Abbaas (may Allah be pleased with him) that when he touched [the Black Stone], he said: “Allahumma eemaanan bika wa tasdeeqan bi kitaabika wa Sunnati Nabiyyika Muhammad sall-Allahu ‘alayhi wa sallam (O Allah, out of faith in You, and in belief in Your Book and the Sunnah of Your Prophet Muhammad blessings and peace of Allah be upon him)”. 
A similar report was narrated by al-Bayhaqi in as-Sunan al-Kubra (5/79) from ‘Ali ibn Abi Taalib (may Allah be pleased with him). These reports were also narrated by at-Tabaraani. 
Many of the fuqaha’ and scholars stated that this dhikr is mustahabb. 
See: al-Umm by ash-Shaafa‘i (8/163); al-Majmoo‘ by an-Nawawi (8/49); al-Mughni by Ibn Qudaamah (3/183); Fath al-Qadeer by Ibn Humaam (2/448) 
Shaykh Ibn Baaz (may Allah have mercy on him) said: 
It is prescribed to say Takbeer when touching or kissing the Black Stone, and when pointing to it if it is not possible to touch it.
End quote from Majmoo‘ Fataawa Ibn Baaz (17/223). 
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 
What should be said when touching the Black Stone? 
When touching it for the first time, one should say: ‘Bismillah wa Allahu akbar. Allahumma eemaanan bika wa tasdeeqan bi kitaabika wa wafaa’an bi ‘ahdika wa ittibaa‘an li Sunnati Nabiyyika Muhammad sall-Allahu ‘alayhi wa sallam (In the name of Allah, and Allah is most great. O Allah, out of faith in You, and in belief in Your Book, and in fulfilment of Your covenant, and following the Sunnah of Your Prophet Muhammad blessings and peace of Allah be upon him).. Then when one has gone around and come back in line with the Black Stone, one should say “Allahu akbar” only. 
End quote from al-Liqa’ ash-Shahri (no. 10). 
And Allah knows best.