How long could slavery in the South have persisted without the war or a different outcome?

[Skill and Chance]

Presumably until the full scale mechanisation of agriculture (thus rendering slavery economically uncompetitive).

You could make a case that happened anytime between 1890 and 1950 depending on the metric.  If an independent Confederacy got involved in WWI, I think the abolition of slavery would be a condition either of military aid from the victorious coalition or of the peace treaty ending the war if they lose, considering every other major player in WWI opposed it.  So, I'm going with the 1910's.