That is handled by a combination of CIV4UnitClassInfos.xml and CIV4CivilizationInfos.xml
In UnitClassInfos, each general type of unit is assigned a class.
One class of Spearmen, one for Warriors, one for Submarines, etc.
In that class is a tag "DefaultUnit" - that is the particular unit of that class that every civ gets to build.
Then in CivilizationInfos, each civ has a block that looks like this :
Code:
<Units>
<Unit>
<UnitClassType>UNITCLASS_MARINE</UnitClassType>
<UnitType>UNIT_AMERICAN_NAVY_SEAL</UnitType>
</Unit>
</Units>
That block says that instead of building the Default unit type of "UNITCLASS_MARINE", they get to build "UNIT_AMERICAN_NAVY_SEAL" instead.
If the unit that you want to make buildable by one civ only is to replace an existing unit, then all you have to do is add another Unit entry to the Civ.
If it is an entirely new unit type that will not replace anything, you will need to create a new UnitClass for it to reside in. Set it's Default to "NONE" and add the Unit entry to the Civ.