Without the Civil War the North and the South would still have a lot of tension. Mostly on their main conflicts of Slavery, Slavery Expansion, and State and Federal rights.
The only way for both sides to get what they want is to separate the country. Where the South could have slavery and more state rights. While the North could abolish slavery and have a strong central government.
As a country the North would be called the Union where everyone would be free, they would have their central government, and can make new laws without the South's disagreements.
In the South also called the Confederacy, they will have slaves to keep up their economy and traditions, a government with more power to the people, and to be able to do things there own way.
There would be an alliance between the two nations, where they wouldn't attack or mess when each other. If slaves escape into the Union they are free and vice versa. Later I think the Confederacy would abandon slavery and they would eventually combine back together.