Yes, we all don't like them so we make sure they collapse early on.
Now seriously, other than a stability buff, what else do you think they need.
Now in monarch, AI Byzantium usually is tech leader until 1100s (AI French is another leader), and usually get education and drama first. They also get gunpowder around 1000.
In human hand, I can lead Byzantium all the way, build every orthodox wonder. The strategy is religious law - cottage economy. Tech: manorilism, engineering-vaulted arches->plate armor, then philosophy-education, then sailing line to clockmaking, found Hanseastic League -- this is too important. After paper switch to limited monarchy then we are good.
Turn 1 switch to religious law, then sign 2 priests in Jerusalem, and Tyre make a settler , both can finish before Arab spawns. First 3 GP join capital. Keep a merchant in Alexandria and Constantinopolis. Capital build Marco Polo's Embassy right after work boat and a worker. Alexandria build settler after 2 work boats and 1 worker. Settle Sicily(Agrigentum). Build a spy and focus on Papal state, we can steal money from Rome. I Also conquered Neapolis by initial swordsmen, although it declared independence once. With Neapolis and Sicily we can get a good foothold in middle of the map.
Before Arab spawns, make roads between Tyre and would-be Dimashq, starve Tyre and Jerusalem to 1 and empty garrison. Let their horse archer capture Type in turn 1, Jerusalem in turn 2, so there won't be flip, and our swordsmen can retake Levant when stability is good.
Found cities in Anatolia and Greece, fill all blanks before 1000, Seljuks spawn in emply space. Send a unit to where Mus would be too. There are 2-3 decent city sites in Anatolia like Trapezus, and inland XXX on iron near deer, copper. Then go for UHV or domination.