I'm fine with inquisitions; I am not morally comfortable with genocide, even in a game like this.
Wait, but when you wipe another culture completely off the map, and none of it is left, is that not genocide? It's not like when you beat another civilization there's any of it left. They are gone. That's pretty much genocide. It is defined as "the deliberate and systematic destruction of a racial, political, or cultural group". Pretty much, when you conquer another civilization in this game, it is deliberate and systematic destruction of a cultural group. So I would say genocide is already in the game.
But along the lines of slavery, you could add to it by being able to enslave part of the conquered populace. And the slave trade thing was mentioned. These would work together. If you don't want the slaves you capture from other civs you can sell them to a civ that does want them. Instead of a slavery civic giving you access to slaves, you would either have to buy them from a civ that's selling them, or conquer another civ and enslave their people. There could be a slaver unit as well. If you're not at war with someone, the slaver unit could go into their territory and steal a small bit of the population to bring back as slaves. Of course that would also damage relations with that civ if you were caught or they found out who was doing it.
Kidnapping? You could kidnap some random high level political figure from another country and hold them for ransom. Or just take part of another civ's population and hold them for ransom. If that civ doesn't want to pay, you sell their people into slavery, or execute the political figure, and they take a happiness hit for not protecting their people. Of course this would also come with damage to your relationship with that civ. And maybe, depending on the civics you're running, you take a happiness hit if your population doesn't approve.
Assassination? You could assassinate other civs' leaders. Maybe not the main leader, but lower level leaders. Maybe assassinate one of their generals and it impacts their army by confusing units for a time. Or assassinate their head scientists and they take a research hit for a while.