No Kansas-Nebraska Act likely would keep the Union together, at least for a good time (extension of a decade or so would be very conservative, I think).
Also helpful might be
keeping Zachary Taylor alive, which would not only prevent the Fugitive Slave Act (meaning less mobilized anti-slavery forces in the North) and possibly a more settled question of slavery in the Mexican territories, but likely a Whig President (Taylor himself) elected in 1852, which also prevents the KNA. Other potential PoDs that might help are
John Brown dying during his raid, and, to a lesser degree, a less sweeping
Dred Scott
If Lincoln doesn't win in 1860, the secession crisis as we know it doesn't happen -- mind you, that doesn't come close to solving the underlying problems, but it does kick the can down the road, giving the US time to unwind the crisis (or make it worse, which TBT is more likely).