If the Union had won a series of decisive battles within the first 6 months of the war that brought about the surrender of most of the CSA's armies and the collapse of the CSA government, such that the Union is preserved, I think we could see a period of great tension - more so than before the war - between the traitorous states and the union states. A sizable union army - probably much larger than the army during OTL reconstruction, would have to be stationed throughout the rebellious states. The highest ranking officers, government officials and other secessionist organizers would have to be tried, and if the Union hopes their victory has long term meaning, then the executions of 100s of the traitors.
In OTL the length of the war, the overall destruction and loss of life killed off the will to wage war in the South, but a quick victory probably doesn't do this. There will be pockets of resistance and guerrilla warfare waged throughout the South - hence the need for a large occupying army.
There needs to be a lengthy period of time where the seceding states are not allowed to sit congressmen or senators, nor electors in the presidential election.
With all this in place, the federal government would then, I think, be persuaded to take several measures that bring about the eventual emancipation of all the slaves. Start with getting rid of any type of fugitive slave laws and pass legislation that rewards people who help slaves to freedom. Then pass legislation that emancipates all slaves that were owned by any southerner who actually took up arms against the union in the war. Next pass legislation that encourages slave owners to voluntarily free their slaves. And then finally (8 - 10 years after the war) pass legislation - constitutional amendments - that completely emancipates all remaining slaves and makes them citizens with the right to vote.