Since this hasn't been locked for necro, I assume mods are cool with this
Give their congress, Generals, and of course good old jefferson Davis the biggest, highest profile trials possible. Make it the most humiliating ordeal possible, but entirely legitimate; they're tried properly, but charged with so much, with so many witnesses, over such a timespan, defense against it all becomes impossible. Hopefully, it will make them look like cruel, uncaring idiots. I don't know a lot about how Davis conducted his part of the war, maybe he was more hands off than lincoln, but but lee was brutal and illegally took free people into bondage.
As for the soldierly, planters, and others? Volunteer soldiers are stripped of rank and property and given a rather harsh jail sentence. Conscripts are given a much smaller sentence and are allowed to keep some decent property. Planters see their estate whittled down to the minimum possible for a family of their size to support, with the lands being carved out between slave and poor white. Normal civilians are simply left alone; the states are still under occupation and getting the commoners pissy will only be a problem