I like to see much more civs than these few possibilities
Mayans or Mayas (i dunno how English spells this central-american civilization), and Incas. I havent't any idea for specific units or leaders, but especially Incas had much greater impact on history than, for example, Iroquis.
Some Uzbeg or Central Asian civilization: In civ1 the mongols represented this civilization with the capital Samarkand. Maybe Timur Lenk could be the leader, and some camel-riding soldiers could be the special units.
A Malaysian or Indonese civilization, with (for example) Sukarno for leader. I've no idea for special unit, maybe some naval unit could be.
Turkish civ, with Suleiman as leader and Jenissary as special unit.
Ethiopian. I've no idea for leader or specific unit.
A Thai or a Vietnamese civilization. We can find out some leader. The special unit would be similar to the Indian war elephant.
Suaheli. This wasn't the right name, but on the place of the today's Kenya, Tanzania and Mozambique was a state, with an advanced cultura. Arabs influenced it, but it was independent until the Portuguais destroyed it.
I could glad for some modern civilizations. When the USA is in, then why Brazil, Mexico, Australia, Nigeria not?. Izrael isn't necessary, this is an Anglo-Saxon city, in fact (The today's USA, Great Britain, Canada, Australia together - they are almost one great civilization, with the same form of government, language, culture and foreign politics.). I wouldn't hurt! Please, excuse me, if i insulted someone.
Please, take back the Carthaginians!
And naturally, we need Mongols, Spains, Arabians, maybe Portuguais, Dutch.