I'm currently playing a game as Byzantium, I'm in 937 and my stability is collapsing. How can I improve it?
Thanks.

Don't even try. Just focus on your core cities (3 in Greece, 2 in Asia Minor + Constantinople). On Emperor I got all 3 UHVs with -100 stability (Apr 25 release).

I'm currently playing a game as Byzantium, I'm in 937 and my stability is collapsing. How can I improve it?
Thanks.

Byzantines are supposed to be unstable and lose all their cities outside the Greek + part of Anatolia core. Read the Byzantine UP, that'll explain it.

What are Byzantine core areas exactly?

Their spawn area on the Reference maps (see the RFCEurope/Reference subfolder). In game terms, Athenai, Thessaloniki, Hadrianopolis, Constantinople, Nicaea and Ephesus, although you can found additional cities in your core area if you want. (Attaleia and Mistra are both useful, Attaleia in particular to secure Crabs for health.)

Byzantines are supposed to be unstable and lose all their cities outside the Greek + part of Anatolia core. Read the Byzantine UP, that'll explain it.

Where is the Byzantine UP?

You can see the Unique Power when you chose civ or in the civipedia. For the Byzantines its "The core of the empire can never collapse due to instability".

If you want a large empire you need manor houses, courthouses and happiness for stability.

I'm currently playing a game as Byzantium, I'm in 937 and my stability is collapsing. How can I improve it?
Thanks.

Courthouses+Manor houses are good for stability

Also pump up Orthodoxy because it gives stability

In my current Byzantium game I managed to keep Alexandria! Amazing!

In my current Byzantium game I managed to keep Alexandria! Amazing!

Yeah, me too. The Arabs never even gave me any trouble at all. Just make sure you are somewhat prepared for the Arabs and VERY prepared for the barb hordes that arrive (a least 5 per turn for about 20 turns) on your eastern flanks right around the same time as the Arabs. The wiped out all my improvements, but I just waited in my cities (with roaming knight to kick their arses) while they fell mercilessly against my castle walls.

In my current Byzantium game I managed to keep Alexandria! Amazing!

Alexandria almost never declares its independance in my games. You do have to garrison it with a few good units though, the Arabs in my game seem to really want that city.