The real problem with Kalbid Sicily is that it has all the problems of Al-Andalus but is smaller and doesn't have a manpower pool.
Al-Andalus survived as long as it did because the locals could always draw upon mercenaries from the Maghreb as hired muscle, even if the hired muscle eventually took over and kept the Iberian territories around as the northern province in a greater Berber Empire after a certain point. Sicily couldn't do that. Sicily also has the problem that the Umayyads tried to staunch by declaring a Caliphate: The ruler of Sicily is always just an emir appointed by someone else, whether by the Aghlabids or the Fatimids, and as such doesn't really have much weight behind his authority in the absence of a bigger power. The island remained most solidly within the Muslim sphere during the period when the island was subject to a strong power with its centre in Ifriqiya - that is, Tunisia. The nature of the western Islamic states - in which an Islamized ruling class sits on top of a vast and surly underclass of dhimmi and a few native conversos whom they do not want to empower - ensured that, unless Sicily survived long enough to somehow convert most of the island to Islam and undergo a big shu'ubiyya revolt which somehow put power in the hands of Islamized Sicilians who could then form their own army, Sicily was always going to be under the thumb of whomever controlled Ifriqiya. This worked fine until 973, even once the Fatimids came in; the Fatimids actually had a large navy based in Ifriqiya, where their seat of power was, and they could just nip across the Med and reinforce their Sicilian proxies.
Then the Fatimids moved the capital to Egypt. The navy went with it. From 973 on, the Sicilians were basically hung out to dry.
Probably what you would need for Sicily to survive is to ensure a strong, persistent power centred in Ifriqiya, which can hold Sicily as a proxy kingdom - that could be a Fatimid empire which doesn't expand into Egypt, or it could be some other Berber empire which gains control of Ifriqiya and figures out what a boat is. It's less likely with the Zirids, who themselves are proxies of the Fatimids; at that point, Sicily is a proxy of a proxy, and bound to fracture.
The manpower problem can be solved like Al Andalus did. Bring up the Berber Tribes. It does bring the same problems the Umayyads faced after Almanzors death but the Islands gets more Islamic and harder target to conquer. Sicily had to deal with the East Romans until the 1040s. Which they dealt with (mostly due to incompetent emperors ,but still).
You are right about something though. The Island is smaller than Al Andalus. It needs either a strong Navy or a North African Power willing to back them up.