OK, I have put quite a lot of thought in this, I believe it would be a really nice addition to the game:
Georgians. They had a pretty long-lasting medieval kingdom in that part of the world, have their own script, language and had a separate branch of orthodox Christianity.
Should share Eastern European architectural style but with having access to Steppe Lancer and Camel Rider lines
Infantry and Cavalry civilization
Units have no penalty when fighting uphill or below a cliff, nor receive bonus damage from their enemies on higher elevation. If this is too OP, then reduced penalty and reduced bonus damage from their enemies.
Trees give 25% (33% or even 50%?) more wood (probably seems a bit useless, but helps with late game clutter, not having to rebuild constantly lumber camps, shorter walking distance, etc)
Towers cost -25 stone but +60 wood (not sure about the third bonus, needs testing)
Unique Unit - Khevsur warrior (infantry with mediocre stats like a long swordsman but with a 2% chance for instakill; Elite Khevsurs get 5%)
if that sounds sketchy which on second thought it kinda does, then Khevsurs could be an infantry that heal themselves when attacking (10-20% of damage done - or even more - gets back as hit points).
Castle age: Caucasian warfare : regenerating trash (skirms, pikes, hussars regenerate 12HP per minute) 600F 450G
Imperial age: Monaspa (Steppe Lancers get +1 melee armor and +2 pierce armor, also attack 10% faster) 800F 800G (dunno if that isn’t too OP)
Outposts cost 10 wood and don’t cost stone; have 2x HP
All that might sound a bit OP for late game but the civ’s overall weakness is towards ranged units. Still needs testing as they sound too OP in late game.
Barracks: militia line up to and including champions
Pikes, but NO halberdiers
obviously NO eagle line
supplies, squires, arson
Crossbows, NO arbalests
Heavy CA withOUT Parthian Tactics
NO thumb ring
Camel Riders (NOT heavy)
Obviously NO elephants
Elite Steppe Lancer
UU + Elite UU
Unique Techs as mentioned
Fast Fire Ship
Cannon Galleon NON-Elite
Demolition Ship NOT Heavy DS
War Galley NO Galleon
Everything except Illumination and Block Printing
Masonry, NO architecture
NO Siege Engineers
Guard Tower (NO Keep)
NO Stone shaft mining
That being said, there is a lot of testing to be done but I believe it is a fairly balanced civ with its advantages and drawbacks, would love to read your opinion on the matter.