I know that they're nomadic and make an appearance in some other games, but I think
The Sioux would make a great addition. They're completely different to the other American civilizations in the game (though calling the Sioux a civilization is open to argument) and provide both a stylistic and geographical opposition to the Iroquois.
A few possible ideas include:
Unit -Dog Soldier:

25

4 (+1)
Ability -Double (& stackable, as usual) flanking bonus (+10% or +15%, I forget)
Replaces -Cavalry.
Building -Nomads Corral: On top of the standard +1

for each source of Cattle, Horses and Sheep, the Nomads Corral provides +1

for each source too.
Replaces -Stables.
Improvement -Teepee: Can be placed outside (or within) a players territory on any tile containing either Cattle or Deer (so Teepees can't be placed everywhere). The Teepee gives all friendly adjacent units +1 healing per turn and a +10% combat bonus. (In the borders of a city, the Teepee tile can be worked, operating as a Camp or Animal Pen for active Citizens).
Requires -Trapping.
This currently replaces nothing. It would currently be effective built beside a Fort improvement, or with slightly greater added benefits, the Teepee could replace the Fort improvement.
Great -War Chief #1: An improved Great General (like the Mongol Khan). The War Chief has

4 (+2) and gifts +1 sight to all friendly units within his radius. Replaces -Great General.
Great -War Chief #2: An improved Great General (like the Mongol Khan). Gives no combat bonus to friendly units, but reduces the horse rider penalties (-33% defensive penalty and -33% attacking cities penalty) both down to only -10%. Furthermore, the War Chief has

3 (+1). Replaces -Great General.
Anybody have any ideas for a unique ability? I've got a couple, but I'd like to see others opinions.