Hmm....slavery was on the decline in the upper South. The leadership of the South was starting to doubt both the economics and morality of it, even in the deep south. Many were staring to see the advantages of having an educated slave population, and also the contradiction implied in that. Once a person is educated, the ability to keep them in bondage is diminished.
Mechanization would also have had a major effect on the economics of slavery. Being able to buy ten machines able to do the work of 50, for the cost of ten slaves, would have been the final nail in the coffin.
My guess is that slavery would have died out in the upper South by about 1880, and in the lower South by about 1910, if not closer to 1900 because of social and economic pressure. There would have been a gradual, natural, elimination of slavery, rather than the disruption of suddenly turning millions out, with no education, no jobs, no property, no means of support, and ruining the Southern economy. And likely, race relations would be much better. Northern racist attitudes would not have been imposed on the South, nor would there be the resentment of having things like the Freedmans Bureau, and all the other "benefits" of Reconstruction.
No telling what the effect would have been if the economy of the South had not been destroyed by the War. All I can suggest is that things would be very different.