Maybe something like this:
PoD: Hung presidential election in 1860 - Douglas wins California, Oregon, Illinois, and Indiana resulting in a tied electoral college. After much confusion, the House of Representatives votes among the top three electoral-college candidates - Douglas, Lincoln, and Breckinridge in this scenario. Douglas is elected as the compromise candidate. He manages to keep the South's sentiments down enough to keep secession from occurring.
Then, in ~1862-63 the Supreme Court rules on Lemmon v. New York and strikes down the ability of states to ban slavery. Outrage throughout the nation and jubilation in the South as it becomes impossible for a state to be free. President Douglas attempts to square the circle through advocating a state-version of his Freeport Doctrine for territories, in which states can at least discourage slavery through legislation. This is not enough, however, and a last-ditch attempt at TTL's version of the Crittenden Compromise - allowing the prohibition of slavery - fails due to the stalwart opposition of fire-eating Southerners who see their victory at hand.
With little recourse, the Free States of America ('FSA') secede from the Union in 1864. Having seen his attempts at compromise fall miserably through thanks to the intransigence of the South, vaguely sympathetic to their motives, and knowing how impossible it is to subdue them by military action, President Douglas lets them go. He's promptly thanked for his service by being sacked from the Presidency in the election that year, replaced by a fire-eating Southerner.
After twenty years of bad feeling that never ignites into open warfare thanks to fear, the American Civil War finally starts in the 1880s, 20 years after the FSA secession, thanks to stronger abolitionist zeal/feeling in the North after seeing the excesses of now-unrestrained southerners and the influence of extremist Southerners who want to spread slavery north.
A few problems:
1. Douglas died in 1861. Okay, this can be butterflied, since it was due to illness. Still, it must be considered.
2. Far more importantly, Douglas was from Illinois. Which will almost certainly be part of the FSA. With his home state seceding, what is he going to do? He can hardly allow this to happen and still remain president of the USA. He won't even legally be a citizen anymore, assuming he "lets the north go".
3. ...which he won't. IOTL he was one of the most radical opponents of secession, wanting to maintain the integrity of the Union "at all hazards". After the bombardment of Fort Sumter, Lincoln decided to call for 75,000 troops to suppress it. Douglas suggested only one change: Lincoln should call for
200,000 troops. This man is
not going to let the Union break apart. He will call for unity. He might be ignored, and if he is, both sides will find him a traitor... but he will
never accept secession.
4. The next president of the USA will not be a fire-eater. It'll be a southern pro-slavery fellow, but not one of the radical fringe. Why would they elect such a nut, after all? They've already got everything they want. Presumably, Delaware, Maryland, Kentucky and Missouri remain in the USA, creating a "super-South". Provided they do not feel like stupidly trying to retake the north (which they wouldn't, they'd just say 'good riddance'), they can basically kick back and relax. No need for radicals to get elected.
5. Southerners would have zero desire to "spread slavery north," and the north would be unlikely to care enough about the slaves to start a war. Even if such a war came to pass, it wouldn't be a civil war, since the combatants would be two sovereign nations.