Not nearly as much of a nightmare as RFC Europe's Byzantines. Stability wasn't an issue at all except for a short while after the Rum were vassalized (should have just annihilated them to prevent the "we want to join our motherland!" unhappiness.
I had close to 80000 gold and generating 2000g/turn in the end...sort of overkill.
Some things I did that were useful:
1. The only early city I built was Germanikeia (1 NE of Sis which prevents its spawn).
2. Gave a city (Sevasteia) to Armenia (so that they will vassalize as well as help me research 2 techs) which helped my maintenance costs immensely.
3. Captured Tarsus early on and spread Sunni in capital. I was 2 turns from the Spiral Minaret!
But in general, I spread religion around so that I can build the wonders. Got Al-Azhar, Imam Reza Shrine, the Observatory, the Workshop, Shalimar Gardens, Qutb Minar, Grand Bazaar, the Embassy, even the Minaret of Jam. And of course Kizil Kule in the capital, the Bagrati Cathedral and Narekavank.
4. Razed Antioch to disallow spawn of PoA, and built a fort on the forested hill just north of it--voila, the only other entrance to Tarsus is blocked off (besides my city Germanikeia).
5. The only difficult thing was to combat the Rum after my soldiers were wounded by the Seljuk barbs. Took a little longer than the Ottomans (who died within 5 turns).
6. All cities destined to flip built nothing but granaries, barracks, blacksmith and troops. (Maybe an occasional church for stability) Right before the spawns, drafts were made and cities were starved so no troops can be drafted by the newly spawned civs. (I starved a size 18 Smyrna all the way down to size 5) Strategic resources like horses and iron were pillaged before spawns.
7. The Fatimids are your friends (stealing 3-4 techs from Alexandria was great), whereas the stupid Abbasids and Zengids kept declaring war.