To avoid the war the Northern States would have to have had more power and influence in the years before it started. The north simply didn't have the strength or the numbers to block or counter the policies made by the southern states.
A reasonable, non-ASB POD would be for the US to not lose the War of 1814 as badly as they did. Starting a war with the British Empire just as the British had beaten Napoleon was utterly stupid. Had the war started sooner, (while the British were preoccupied with Napoleon, which would have kept the bulk of their forces busy in Europe until Napoleon's demise in the spring of 1814), been avoided altogether, or had the US made a better show and their armies not been completely crushed in the Canadas, Michigan, New Ireland (OTL Maine), upstate New York, or in the Ohio valley, the North would have been at the very least the equal of the South, and perhaps would have been the dominant region of the United States in the mid 19th century.
As it happened, the US lost the war, and in the peace treaty lost New Ireland, the remainder of the St. Lawrence watershed, and everything north of the Ohio river, west of the Appalachians. This included several territories that had just been admitted as states, such as Ohio and Indiana. (Currently known as the province of Ohio. The industrial heartland of the Kingdom of Ontario*.) The British also took all of the Louisiana Territory north of either the Missouri River or the 42nd parallel, with the new border being set at whichever of those was farther south. The war and the humiliations that followed did great damage to the north, but hardly affected the south, apart from the effects of the blockade enforced by the Royal Navy.
This caused great resentment in the North, who blamed the south for getting them into the war, and for the devastation and the humiliations that followed it. Indeed, the resentment was so great even during the war, that several northern states, mostly in New England, openly contemplated secession, and had the war continued for any longer than it actually did, would probably have left the Union then and there.
(*OTL Ontario east of Lake Superior, Ohio, Indiana, Michigan, Upstate New York, and Illinois. One of the three North American kingdoms of the British Empire, the others being Canada** and Borelia***.
**OTL Quebec, Vermont (the north half), Maine, New Brunswick, Nova Scotia, Newfoundland, Labrador, Baffin Island, and Prince Edward Island.
***The rest of OTL Canada and the US west of the Mississippi, north of the Missouri/42nd parallel, plus the entirety of Wisconsin and Minnesota.)