The practice most likely would have been brought to an end some time back then. It's hard to imagine the US having had slavery say in 1900, 1910 and so on.
I see no reason for believing that.
Of course, to get to 1900, we must ignore the fact that the Civil War was inevitable just due to geography -- as a matter of agricultural necessity, slavery
had to move north of the Mason-Dixon line in order to move westward, and the North was largely and increasingly opposed to slavery for a variety of reasons. "Bloody Kansas," or something very like it, would have happened regardless.
But suppose that the sectional crises had somehow been resolved so that slavery was still around 40 years later:
It is no accident that the advent Industrial Revolution brought with it the Labor Movement, which arose in part to combat real exploitation of factory workers, in the form of low wages, dangerous working conditions, etc. Many industrialists were notably exploitative of their workers. Things like sweat shops, company towns ("I owe my soul to the company store)", share-cropping (coupled, for blacks with Jim Crow laws), Chinese railway labor, and so on -- these were in many respects little different from slavery, even after the war.
In that context, consider if slavery were still prevalent in, say, 1880 or 1900. The value of a slave in the Industrial Revolution would most likely have increased in much the same way that the value of slaves increased after the introduction of the cotton gin. Slaves would have represented cheap labor performed by people who had no right to leave, and who had no recourse if they were to complain about working conditions.
It could even be suggested that had the South been more receptive to the Industrial Revolution, and not so devoted to agrarianism and the plantation system, they might possibly have won their independence by having created a slave-powered industrial base -- the lack of which, in the actual event, probably cost them the war.
