Have a date in mind? The south was losing the war almost from the very beginning. An assasinated president, murdered by a southerner most likely in the pay of Jefferson Davis (or so it could be painted) would be a rallying point, a 'win this for our martyred Abraham Lincoln' kind of thing. In the end the south would still have lost.
I think that if Lincoln had died, say in 1862, before Sharpsburg, the North would have made peace. Remember, at one point, there was a strong peace movement.