There was a flurry of compromise proposals in late 1860/early 1861, but they were all doomed to failure. By the time secession took place, the South was set on independence and no amount of concessions by the North on slavery was going to persuade them to come back into the Union. In turn, Lincoln was absolutely determined to keep the Union together and there really was nothing for the South to offer him. IOTL, they offered to pay for federal property, assume a portion of the pre-1860 national debt, and a whole host of other things, but it didn't matter.
The two sides were dead-set on mutually exclusive goals. The South was bent on independence and the North was bent on union. War was inevitable.