From Durres, Albania (yes, Austria would need to take over Scutari (Albania) in 1877) Cyrenaica is only a couple hundred miles away. Maybe in 1877, Austria splits Libya with Italy and Italy also gets Tunisia, which Garibaldi wanted but the French did not want him to have. From Benghazi and Tobruk, Austria can build a railroad to Tobruk, Abeche and El Fasher, Darfur, conquering Baguirmi. Railroads are not hard to build over desert. Austria can get direct access and title to a huge chunk of Africa, probably extending all the way to the Congo River, where it bumps into King Leopold's claim, and the Ubangi, where it runs into Italy, which likely will be doing the same thing. As we all know, Central African Republic is rich in diamonds and gold, and Chad has a large enough population to work those mines, so this could mean a workable colony.
Given the low population of Cyrenaica, I would expect the Kanem people of the Sahel to quickly overwhelm the Arab population of Cyrenaica and radically de-Arabize Cyrenaica. Austrians and especially Hungarians, Croats, Bosniaks and Albanians will also migrate to Cyrenaica, turning the place into an imperial polyglot.
Much the same thing will happening in Libya and Tunisia. Italy will soon see how easy it is to build a railroad across the Sahara and scramble to secure it's section of Chad before France gets it. Kanuri and Ubangi people (Ubangi converted to Catholicism) will be migrating to Tripoli and Tunis by the end of the 19th Century. France would quickly follow suit with Trans-Saharan railways, leading to development of French West Africa ITTL and Africans diluting the Arab and Berber populations of Algeria. In all of these cases, maybe only half of these Africans will be Muslim. This means big changes in North Africa west of Egypt ITTL as it is integrated demographically and culturally with Central and West Africa. rather than the Middle East. Only Morocco, remaining independent until the 1900s, might escape somewhat, being overwhelmed by immigration from Africa and France. But it is Austria which has the most reason to get that particular trans-Saharan colonial ball rolling ITTL since Austria needs to access Africa without doing so by sea.