That reminds me of what happened in Brazil. It wasn’t until 1888 that it was abolished, but economic changes and the international context forced its decline for decades.
Much like that, yes. Key defferences would be that the USA is a federal union (and, lacking the Civil War, states' rights are not discredited!), and also has a very stable legal order-- which will actually work
against abolishing slavery. The federal government can't just decree "and now we end slavery". It remains the prerogative of the states, so you either need to pressure the Southern bloc, or you need enough states on board to amend the Constitution. That last one is extremely tricky: there were 15 slave states in 1861, and you need the approval of three-fourths of all the states to ratify an amendment to the Constitution. That would require you to have 60 states, assuming all slave states will vote to retain slavery. There is the potential for three more slave states (New Mexico, Arizona, Oklahoma), but those won't get admitted until we're in the 20th century anyway, nor are they particularly into slavery. (Should it come to it, you could sway them to agree to entry as free states in exchange for some lucrative pork barrel, I think.)
Of the 15 slave states, you can probably sway the Upper South to vote against slavery as well, at least eventually. As it becomes clear that the whole world is turning against slavery, and again with the prospect of some interesting federal favouritism in exchange for turning against slavery, Missouri, Kentucky, Tennessee, Maryland and Delaware can probably be persuaded to vote with the North. You'd have to offer them a
lot, though. Think of subsidies to set up manufacturing and industry, to compensate for slavery ending, plus pre-arranged contracts contracts for said industry to provide a lot of whatever the federal government needs. That's still cheaper than some mass scheme of compensated manumission (which the Deep South would demand). Also, the co-operation of these Upper South states is based entirely on the sort of "gradual emancipation" scheme I suggested. They'd be far less likely to go along with immediate abolition!
Anyway, at that point, you have just ten states left in the "firmly pro-slavery" camp, which means you can get to the abolishing part as soon as the Union grows to 40 states. There being no West Virginia due to the lack of the Civil War, that means the 40th state is Montana-- admitted in 1889. I'd expect a Constitutional Amendment to ensure gradual emancipation to be passed in 1890. The Deep South will be furious, but its rage will be entirely impotent.
(There will be those who argue you'd be able to get Virginia to side with the North as well--especially since less-supportive-of-slavery West Virginia is not cut off from the rest of the state--and I'd agree with that, but the North won't waste resources on buying Virginian co-operation. It wouldn't make a difference, because the two states to enter the Union prior to Montana are the Dakotas... and they did so just a few days earlier! Spending lots of resources to curry favour with the Virginians, then, would be a
very expensive way to abolish slavery four days earlier!)