It depends heavily on the 'how'. As
@Joshuapooleanox points out, the whole conflict had been brewing for decades. Without changing things early on, you will still see a largely northern movement like the Republicans arise. Demographically and economically, the north was just going to overtake the south, and that was always going to have consequences. Much like the rest of the Western world, the north was becoming ever more opposed to slavery as a concept, but besides this, the north historically favoured policies that would give more economic and political control to the federal government-- something the south didn't want. Slavery was the central issue, but two completely different views of what the USA ought to be like were going to clash here, no matter what.
I can see three basic ways to avoid the conflict:
1. Have the USA be more inclined towards "states' rights", even moreso than in the OTL antebellum period. If it's pretty much accepted as a given by all sides that the federal government cannot ever have the power to abolish slavery (or otherwise interfere in the internal affairs of states), the south has no reason to secede. This option would have to include constitutional guarantees of state sovereignty, likely including slavery explicitly. In OTL, Lincoln literally said he had no intention of interfering with slavery in any way, and the south still seceded. They were downright paranoid about the issue.
2. Have the USA be more centralised, instead. A USA that goes heavily Federalist early on (the way Hamilton wanted it) and then gets handed over to other defenders of such policies... well, that would be a different USA. You'd have high tarriffs from the outset, subsidies for national industry, that kind of thing. You end up with the kind of economy that is less reliant on slavery early on, and the north will gain political supremacy earlier, too. Slavery can then be limited or ultimately even abolished before it gets to the point of a civil war.
3. Have a Republican party emerge weaker than in OTL. Ultimately, a weaker republican leader than Lincoln gets elected. The South still threatens to secede, but the weaker republican leadership accepts an ATL version of the Crittenden Compromise as the least bad way to avoid war. The constitution gets amended accordingly. This is a lot like option 1, except with less early changes (and thus less butterflies). I'm not sure how easy it is to achieve, though.
Obviously, the first and third options avoid secession and war by giving the slave states what they want. The results of this should be obvious: contitutional guarantees for slavery, would entail that slavery gets to exist for a long time to come. Option 1, with the early POD, means that such guarantees are given at an early stage, however. Unlike the Crittenden Compromise, they msy not be worded in such a way that later amendation is explicitly made impossible. Also, the guarantees may be limited to existing slave states, so that slavery can still be kept out of territories and future states. Option 3, on the other hand, would entail that slavery is guaranteed in the south, in all future southern states, and cannot ever be abolished by the federal government. Even altering the constitution to
make abolition possible would be prohibited. So option 3 basically gets you late-onset
Decades of Darkness.
Option 2, on the other hand, gives the north what it wants, and makes an early end to slavery possible. The completely opposite direction. But no matter what, to prevent the civil war, the simple fact is that the issue of slavery has to be settled - one way or another - before it gets to the point of secession.
