The question isn't so much "Why didn't the Centauri conquer Earth?"
as, "Why would they have WANTED to?"
We're kind of off the beaten track, and there's little logistical or
tactical value to a base here; up until the last couple hundred years, we
didn't have a technological base they could exploit, and when we finally
did get one, the Republic was already beginning to shrink and lose its
tendency toward expansionism. Basically, we fell between the cracks, and
for something as substantial as acts of conquer, there have to be solid
goals, either real or imagined.