I know this is a really old thread, but for some reason it's been on my mind a lot, so I finally decided to take a stab at this.
For most civs, the adjectival form will be the same as the in-game civ name, e.g., a Bannor Champion, a Hippus Knight, etc., just as we refer to "the French" and "a French city." For those civs whose name ends in an "s," the adjective would be the singular form of the name, e.g., Amurites --> an Amurite Warrior, Mercurians --> a Mercurian Angel, etc.
So I've focused on the name of the nation. Some, like the Ljosalfar and Svartalfar, were pretty obvious, from the associated Norse mythology. The rest I just guessed at what might make sense. I can't say I've been consistent in terms of grammar, so anyone interested should feel free to offer suggestions.
Here goes, with explanations in certain cases. I've included civs from modmods also.
Amurites – Amur (on analogy with such formations as Canaan/Canaanites, Edom/Edomites, etc.)
Archos – Archosia, with the adjective being Archosian (I think that's what's used in the mod)
Austrin – Austra, maybe Austrinia?
Balseraphs – Balseraphia (sorry, best I could do. I know "seraph" has Biblical Hebrew origins, but no idea what "land of the seraphs" would be)
Bannor – Bannoria, Banngard, or Bannheim -- I lean towards Bannoria, but suggested the others for variety, or possibly as the nation's name among other civs
Calabim – Calabistan or Calabia
Chislev – I always thought Chislev sounded Slavic, so Chislevgrad or Chislevska, and to be really cheeky, Chislevan Rus’
Clan of Embers – This one was harder, but a few possibilities: Emberland, Emberia, or Embria; Emberian or Embrian for the adjective
Cualli – Cuallia (my preference) or Cuallistan
Doviello – A few possibilites here: Dovheim, Dovgard, Dovmark
Dural – Duralia
Elohim – Elohia or Elohistan, following the two possibilities for the Calabim
Grigori – Grigoria
Hippus – Hippustan
Illians – Illia
Infernal – Enfer, Gehenna, Tartarus, and, just for fun, Mordor
Jotnar – Jotunheim (again, from Norse mythology)
Kahdi – Kahdia or Kahdistan
Khazad – Khazad-Dum (couldn't resist) or, more conventionally, Khazadstan
Kuriotates – Kuriotatia, or maybe Kuriot
Lanun – Lanunia
Legion of D’Tesh – For the national form, maybe D'Teshia, or D'Teshland? The adjective used in-game is D’Teshi, so I'll stick with that
Ljosalfar –Alfheim (from Norse mythology)
Luchuirp – Luchgard or Luchmark; i also thought about Nidavellir, from Norse mythology, but that's an alternative name for Svartalfheim, which goes with the Svartalfar below
Malakim – Malakistan or Malakia, like the Calabim and Elohim
Mechanos – Mechland
Mekara Order – I think they would call their country Mekara; The adjective used in-game is Mekaran, so I'll keep that
Mercurians – Mercuria (didn't want to use "Mercury")
Mazatl – Mazatlan (couldn't resist)
Scions of Patria – I think the way the Byzantines called themselves Romans while foreigners called them Byzantium and Byzantine, these guys would call their country Patria and themselves Patrian, while foreigners would call the country Scionia and use either Scion or Scionian for the adjective
Sheaim –Sheastan or Shealand. Neither one rolls of the tongue, but hey.
Sidar – Sidaria, Sidgard, Sidheim, Sidmark -- I think Sidaria is best, with the others being names in other civs' languages.
Svartalfar – Svartalfheim (also from Norse mythology)
So, that's it. Not sure why I've been thinking about this for a while, but there it is.