Start with a Norman Sicily not willing to give up Tunisia, leading to an Early Almorahad disinterest with the eastern Maghreb, choosing to focus primarily on Iberia, with a strong garrison around Marrakesh. With greater cooperation with the existing Arabo-Spanish Taifa nobility, a capable Almorahad leader could cement power and begin to re-centralize the state, easily defending everything south of the Tajos River, and more often than not controlling most up to the Duero and Ebro Rivers. The Asturian kingdoms of Galicia, Leon, and Castille (as a stunted Portugal would have been absorbed by Galicia), as well as the Catalonians in Aragorn would still be in the throes of the Reconquista, though the Basques of Navarre may be a possible friend of the Muslim state. Continue solid leadership with continued revenue from Northern Africa (perhaps even a reconquered Tunisia as the Sicilians began to loose footing) And the Almorhads could see the growth of a profitable Mediterranean trade empire, giving Genoa competition for the markets of Provence and various Italian city states.
With Cordoba being a continued place of knowledge and education with a keen mercantile interest, Sevilla could become a center of navigation, with the Moors making ventures such as the Canary Islands and the Azores. They could reach India by 1300 and probably hit North America within a century.