Well, to my knowledge, some of the countries that abolished slavery without war (like France) did it through totalitarian governments that held more power than the US government ever has.
These countries (likely...as I'm only going on the European countries that abolished it) DID GO THROUGH CIVIL WARS, they just weren't about slavery. To an extent, the US is such an outlier in terms of countries, in that we're 1) Fucking huge...literally, the US is like the 5th biggest country in the world 2) Filled with a bunch of different religious dissidents, so there is no one true majority (I guess WASPs would count, but not sure) unlike other countries where there is a clear cultural/racial majority 3) We were a new country (I've seen some terribly stupid posts by certain African-American activists where they are trying show how recent slavery was, yet they never mention that this country has NOT had slavery for 2 times as long as we had Slavery).
To a large extent the American political system was still being created (as I mentioned in my post re: Missouri Compromise) and thus it was always unlikely that such an important issue would be able to be solved with mere diplomacy. Many tried though, but again, the Southern Slave-holding states felt that abolishing slavery would DESTROY THEIR WAY OF LIFE, so nothing short of kidnapping all the Southern senators and forcing them to sign an agreement on the pain of death, we weren't going to be able to solve that issue without war.
PS To anyone claiming that Slavery wasn't the cause of the War and using the states' right argument, it's wrong (but not 100% you're bat-shit crazy wrong). Southern slave-holding states were so worried about slavery being outlawed that they wouldn't even allow a new state to join the Union without "balancing" the books. They didn't require these states to have certain economic obligations to the South. They didn't require these states to increase inter-state commerce. They required these states to legalize slavery. That's what the war was about.
I mean, if you wanted to make the argument that it was a cultural war on the macro level, I can buy that. We're kinda going through one right now.