The viability of slavery ended with the advent of labor saving devices.
Simply put, as soon as tractors, etc, came along, slavery would have been obsolete, and would have eventually just faded out.

I gave you that answer because I read several Declarations of Secession of some Southern States.  Most of them gave reasons for slavery.
Some of them were:
Black people, by virtue of skin color and native climate, were more suited to manual labor in hot, humid, very sunny conditions.

Ok, so that was one reason.  It is late and I haven't had enough coffee, but my study of the Civil War and the Declarations have convinced me that slavery was already on the way out, even if there had not been a Civil War.  Slavery was just begging to get replaced by machinery that could do the same job.
As soon as that happened, slavery would most likely be quickly phased out, and at worst, slowly fade out.

History was and is written by the victorious.  The Civil war was not fought over slavery as our books now tell us.  It was a good recruiting tool for the war though and the differences in opion on the topic was a lead factor leading up to the war.  A check of history will show you that most of the sourthern states had already agreed to abolish slavery if not already in law then in principle.  Most of the southern men killed in thw war were poor whites who had no need nor could afford slaves.  It would be kind of like us fighting so that our bosses can keep their Mercedes, not me boy.  The south saw the war as a war of northern aggression and for the most part still does.  The north saw it as the war to perserve the union that our forefathers established.  Hate to call who was right on that one, both have a point.

Like most wars, the spark that pushed that one was economics.  The ferderal government passed a tariff on all agricultural exports thus forcing the south to only sale to the north.  English automation allowed higher payments for raw material possible. This was the straw that broke the camels back.  That is why England supported the south.  They had abolished slavery long before 1860. As for the Mexicans taking back their land, I don't recall US troops at the Alamo.  Fact is that even the defeated and demoralized Confederate Army was better equiped and better trained than any army in the world at the time.

Tom Predicts:

If the south had have won.......Slavery would have died before the end of the next century anyway.  Whoops happened anyway.  (Dr. King)

Most of the black population would be in the north trading slave cabins for slum housing working in northern factories for not even enough to feed them.  Whoops, happened anyway.

The two countries would unite in the early next century behind a more states rights leaning Federal Government.  Guns would be illegal in the North and on everones hip in the South. (Happening anyway)

Now that I think about, maybe things wouldn't be much different.