This is one of those questions that is near impossible to answer.
The best I can give you, based upon my reading, is that it is likely that slavery would have continued for quite a while longer. Over time, though, it would have held a diminished role in society as the South industrialized. The advent of the assembly line would have further pushed the decline.
Holding slaves was a morally bankrupt AND expensive endeavor. For a long time, the cost benefit analysis for slave owners was that they could get years of work out of a person without wages. Eventually, with technology, this would have made the institution less of a good "investment," combined with moral pressure as most of the Western world divested itself from slavery.
So, you'd likely see a more pronounced version of our de facto slavery with migrant farm workers in the United States.