Are you thinking of Islamic forces overpowering Byzantium and installing an Islamic rulership? Or of a Byzantine Emperor voluntarily adopting Islam and pressuring his subjects to convert as well?
For the former, either of the Arab sieges succeeding could have seen (parts of) Byzantium added to the Umayyad Caliphate, with perhaps a later restoration of Byzantium under a breakaway "Byzantine Sultan."
For the latter, I'll leave it to the Byzantium experts on the board to suggest an Emperor (or imperial claimant) who may have been tempted to convert to Islam at some point.
Technically, when the Byzies fell in 1453, the ottomans claimed the title "Sultan of Rum" which means Sultan of Rome, which is kind of what you're going for? Otherwise it's ASB.
I mean, if Islam arose as a sect of Christianity, such as miaphysitism that gained converts within the empire, I can see an emperor following that particular branch (much like Anastasius was a Miaphysite), but other than that, Islam in its OTL form was never going to win the conversion of a Byzantine Emperor.
Wasn't Islam viewed as a, very successful, Christian heresy for centuries, I believe up to the crusades, instead of a separate religion entirely.
Wasn't Islam viewed as a, very successful, Christian heresy for centuries, I believe up to the crusades, instead of a separate religion entirely.
Perhaps expanding from Islamic Sicily?Have we considered the possibility of an Islamic caliphate extending to the city of Rome itself?
I'm not much of a medievalist, though I have taken a couple classes on Islamic history, so take what I'm saying with a grain of salt. But could it be possible for the Umayyad splinter that overtook Spain to extend its reach to the Italian peninsula somehow? I will leave discussion of this point to those who know a lot more about medieval history than I do (I tend to focus on modernity with a special focus on American politics), but it seems intriguing to me.
I realize that this idea kind of goes against OP's question, as they were asking about an Islamic Byzantine Empire (which was really the Roman Empire, just identified by a different name in modern historiography for clarity), but the idea of an Islamic state in Rome itself intrigues me.