I suppose you could have some Druze revolt catch on among Damascus's disaffected urbanites (laid-off Janissaries, soldiers upset about not having pay, proto-Nahda intellectuals) and then take the province by storm, something like what happened with the 1925 Syrian Revolt. This is all the more likely if the Ottomans suffer some catastrophic defeat in the Levant (e.g. loss of Iraq to the Afsharids or Mecca to the Egyptians) that makes Constantinople's security umbrella seem less valuable.
In that case, though, the urban/landowner elites are likely to dominate any new Syrian state through varying degrees of alliance with Druze notables, who even in OTL could command large, loyal, and well-armed military forces. This doesn't however, necessarily imply Muslim dominance-- a large contingent of Christian landowners (Armenians, successful Syriac families, Maronites) lorded it over plenty of Shi'a peasants along the Mediterranean coast. So the three most powerful groups are likely to be urban Sunnis, the Druze, and urban Christians. I can't see the form of government being anything other than a Muslim monarchy (see: Muhammad Ali) but it's likely the founders of this Syrian state would have some early disputes over whether a Druze of some illustrious lineage or a
sayyid Sunni gets to be the first Sultan. Feudalism would likely remain a prominent social problem, with rural Christian and Shi'a populations suffering the most because of it.
Yeah, Europe have never raised a small minority with little power, to be the ruling elite in a more or less overt protectorate *nods wisely*
While it is within Europe's power to create minority-led native protectorates, it's hard to see that being the outcome of a Greek-style Syrian War of Independence. It's maybe possible if European State X intervenes at the war's midway point (maybe a point at which the Syrian revolt was starting to falter) under the pretext of saving Christians and then forces the Ottomans to make Syria a mega-Lebanon. Even then, ensuring unchallenged Christian dominance would likely require State X to invade their new protectorate and militarily break the power of competing groups-- at which point the "independent" Syrian state will owe more to European intervention than to its original revolt. Both actions would tank the Ottomans' relations with State X completely, because while the Ottomans could reconcile themselves to losing such marginal lands as Bosnia and Libya in the 20th century, they might not be able to accept losing the old homeland of the Umayyads in the 19th century.