I think this is an awesome idea!
For the Aztecs, you could have Eagle warriors in the Ancient Era, Bandidos or Rancheros in the Renaissance, and (hehehehe) Zapatistas in the Modern era!
Eagle Warriors would replace, oh, I dunno... axeman? Jaguars replace Swordsman, right? the two should be contemparary, with perhaps a defence/offence distinction.
Bandidos/Rancheros should replace Grenadiers, and should look like Pancho Villa (look'im up)!
As for Zapatistas, well... it'd be so sweet if they were like the CivII guerrillas, except only the Aztec can have them *drooool*... Thinking along those lines though, maybe, whenever a rival city's population is over 50% Aztec, there is a 1/4 chance of a Zapatista spawning in the city radius? and, although it's under your control, it won't move away from the city radius, and will automatically disappear as soon as that city flips?
Or, on a completely different approach, they could be relatively weak units with a special Bombard-ish ability that shoots other units but not city defenses (to represent guerrilla tactics)...
For the Inca, some sort of Llama-cavalry unit would be AWESOME (if extremely innacurate

)!! Naw, seriously, the Inca should have some sort of worker unit who can improve Mountain tiles. Even better, they should have a special Worker who can build roads through Mountain tiles!
Another possible Ancient era unit which might be overpowered is the Amauta; Amautas were a little bit like wandering "wise men" who told stories. Since the Inca never developed a written language, you can imagine how important these "keepers of culture" would have been. Anyway, the units could work kinda like missionaries who can spread your state religion (whatever it maybe at the time), but can also explode (in your own cities only) for a little culture boost (25-50culture maybe?).
A good idea for their Renaissance unit would be the Guardia Bolivariana... They'd replace the Cavalry, and for their looks, Im sure there's lots of pictures of Simon Bolivar floating around. They should probably have some extra bonus in the vein of decreasing war weariness (or maybe you can draft one citizen whenever these guys are in a city?), bacause of the ardent patriotic fervor that Bolivar's liberation incites (even today) in large parts of South America.
For the Inca Modern unit, you could make Tupac Amaru, yet another guerrilla unit (sorry!)!
An idea for another Russian UU... KGB agent! I'm not sure exactly what it would do, but it would (obviously) replace the Spy, and perhaps just have more espionage abilities. And she (yes, she) should look like the CivII Foreign Advisor, beret and all!
I'll probably think of a few more and post them later... hope you like these though!