With a POD between 970 and 1000 AD, can Muslim rule in Sicily be sustained into modernity? It doesn't have to be the Kalbid Emirate, which I'm fairly sure is doomed.
The obvious answer would seem to be "avert the Normans," but that doesn't solve the problems with other western Islamic states in the medieval period (al-Andalus), namely foundational instability and factionalism with little hope of reinforcements. Especially in Sicily's case you add that they're right on the Pope's doorstep and an obvious target for anyone hot to win Rome's favour by kicking around the Muslims. If the Normans don't come along, someone eventually will.
Can the issues be overcome? Can Sicily remain Muslim in a long-term way? Or is it too late?