The South tolerates Lincolns 1860 win, and never secedes; what changes?

[Skill and Chance]

TBH I don't think this is reasonable, but if it somehow happens, it probably all hinges on Virginia and its military establishment refusing to secede.  There would still be a revolt on at least the same scale as the Whiskey Rebellion in the Gulf Coast states, but McClellan and Lee crush it together in a few weeks so it doesn't snowball. 

Unfortunately, this also likely means a much slower abolition of slavery.  The "deal" that involves the South or at least enough of the South tolerating Lincoln would likely include the Corwin Amendment, which would permanently remove the potential to abolish slavery federally, so it would have to go state by state.  In a world where individual states are permanently more powerful, I could see New England et al. effectively "sanctioning" Mississippi et al.  As the North industrializes, the economic pressure would mount and probably force abolition circa 1900-1910.  Alternatively, with accurate guns being mass produced, the possibility of a successful slave revolt in one or more Southern states is intriguing, especially if the wealthiest states/cities/families in the country were cheering them on.

[Skill and Chance]

There was no chance whatsoever that either the election of Fremont, Lincoln, or any other hypothetical Republican President in the 1850s or 1860s would be tolerated by the majority of the South. Even if you successfully stop Tennessee or North Carolina from secession, it's an absolute certainty that South Carolina, Mississippi and Georgia still will, and it's hard to imagine Texas or Florida not dong so either.

I'm not sure about a "great man" theory of history, but as long as the Union keeps Virginia in any of these scenarios, Grant, Lee, and Stonewall Jackson all fighting together on the same team means the "war" against the severely underdeveloped Gulf Coast state would be more like suppressing some riots vs. the multi-year horror it was.