(Shia Islam view)
Shia believes the black stone is more than a stone and also believe grave of prophet and Imams are more than the black stone.
Also Quran says the shirt of prophet Yusuf (PBUH) did cure the blind eyes of his father. So there are more sacred things that are blessed and can be kissed.
Dawud ibn Salih says: "[The Caliph] Marwan [ibn al-Hakam] one day saw a man placing his face on top of the grave of the Prophet. He said: "Do you know what you are doing?" When he came near him, he realized it was Abu Ayyub al-Ansari. The latter said: "Yes; I came to the Prophet, not to a stone."
Ibn Hibban in his Sahih , Ahmad (5:422), Tabarani in his Mu`jam al-kabir (4:189) and his Awsat according to Haythami in al-Zawa'id (5:245), al-Hakim in his Mustadrak (4:515); both the latter and al-Dhahabi said it was sahih. It is also cited by al-Subki in Shifa' al-siqam (p. 126), Ibn Taymiyya in al-Muntaqa (2:261f.), and Haythami in al-Zawa'id (4:2).
Reference and more evidences:
