I'd say around 30 years. I think the only place slavery really hung around for a long time was Brazil.
Of course, their are some Mid East countries where it goes on today (usually the Religion of Peace enslaving Christians), but not as a national institution.
I blieve it would depend on outside influence and how the confederacy would react to it. For most slave owners it was a convenience issue more than an ecomomic one. Every one looks at the large plantations with their dozens of slaves and forgets that most slave owners in the south didn't have massive plantations. Most slave owners had a few slaves and a considerable percentage of those used slaves as household help. Where were the replacements for the cooks and nannys and maids to come from? Without outside influence the use of slaves as household help could have continued for decades into the 20th century.