What where some attempts at compromise to avoid secssion and war?

First, the Missouri Compromise of 1820, which managed to keep the situation balanced for thirty years, until the acquisition of vast new territories after the Mexican War. This required a new compromise, which was cobbled together rather desperately in 1850, and did not hold.

In the absence of any better suggestions, Senator Stephen Douglas of Illinois proposed that the people of each new state should be allowed to vote on whether it would be slave or free ('Popular sovereignty'). This suffered from a dangerous flaw. By allowing one state to vote at a time, it encouraged gangs of outlaws from both sides to descend on that state, to try to interfere with the ballot and terrorise local citizens. The first time it was tried, in Kansas, it led to serious bloodshed.

Following the inflammatory verdict of the Supreme Court in the Dred Scott case, declaring slavery to be legal in every state of the Union, the John Brown rebellion, and then Lincoln's election on a ticket of no new slave-states, war became inevitable. A last attempt at a compromise was presented to Lincoln, who rejected it because it could have allowed new slave-states.

By the time Lincoln was inaugurated in March 1861, the Confederate States of America had been proclaimed in Montgomery, Alabama, and the first shots of the war were fired one month later.