I'm not sure what the value is that triggers the "lack of slaves" modifier. From looking at defines.txt, I'd guess that every point below this value will give the Civic faction +1% influence to a maximum of 20%, but that's no more than conjecture (haven't actually played the game in quite a while...).
Whenever you capture a province with a different culture/religion from yours, a portion of its citizen population will become slaves/freedmen. So, to increase your overall number of slaves quickly, the easiest way would be to conquer something.
Half goes straight to your capital and the rest is divided equally amongst your (controlled?) provinces. This means that you can get some incredible population numbers in your capital as a barbarian one-province minor: subjugate the barbarians around you for a while and you'll eventually build up quite a significant population in your only province. It's probably the most effective way to go about running a barbarian country in the middle of nowhere, IMHO.
Actually, I feel like starting up a game to do just that, now...
