The assassination of Abraham Lincoln in 1862 and the CSA victory at Gettysburg in 1863 demoralizes the North. Key Union cities, including Washington, DC, are occupied by Confederate Forces. The War of the Rebellion becomes The Continental War, as more states attempt to secede, some to join the Confederacy, others to go their own way. But what's left of the Union still has more industrial resources than all the seceding states combined. After the 1868 elections, the Federal government is in the hands of "Union or Death" fanatics who vow to stop at nothing in order to preserve the Union. Meanwhile, the CSA, which was never the loose confederation its founders envisioned, becomes a military dictatorship under its unwilling ruler, Robert E. Lee.
Lee had supported the Confederacy out of loyalty to his home state of Virginia; he had always been opposed to slavery. He had even attempted to persuade the Confederate cabinet to offer slaves freedom in exchange for military service. In 1870, faced with a seemingly endless war, the man who would be known as The Father of the Confederacy, uses his extreme popularity (and not a little military coercion) to force the CSA to accept an end to slavery.
This one stroke reverses all the forces that were destroying the Confederacy. The CSA armies, desperately short of manpower, receive a vital infusion as thousands of newly minted "citizens of color" heeded the call of "Father Bob" to join the colors. The Great Powers in Europe, always secret backers of the CSA, could now support it openly with naval and military forces. And having lost the moral high ground, the "Rump Union" loses the support of its own citizens for continuing the war.
A century later, the Confederate States of America is a multiracial democracy, occupying most of North America, and with member states on other continents It is the proud boast of CSA patriots that every state joined the Confederacy voluntarily. Little is said of the massacres that accompanied the annexation of Mexico.
The CSA is also the world's dominant power, both through military might and moral example. The role of African-Confederates in winning the war has permanently changed the relationship between black and white (and, after the Expansion, between black, white, and brown). Moreover the example of the Confederate "unity of peoples" has changed racial politics all over the world. A notable exception is the tiny "racially pure" United States of America.