What about changing just matriarchy to lineage, as matriarchy is so rare that it's existence in history can't be definitely proven. At the time patriarchy emerged there were probably a focus on lineage in non-patriarchies as well. Lineage would thus be more egalitarian than what patriarchy is.
If there's a "Patriarchy" civic, any player would probably wonder why there isn't a Matriarchy also, even if that's historically not very accurate... So one way to have it would be to have a non-distinct "gender-based rule" or "Patriarchy/Matriarchy" or whatever. Another would be to have a Matriarchy civic - but with exactly the same effects as Patriarchy (making Patriarchy vs. Matriarchy mainly a cosmetic choice, but why not?) :]