The war was on but Lee had surrendered, so things were looking bad for the south.
My question is, what would have happened if Lincoln had been killed while the south's army was still strong?
Outside of Virgina, where Lee and the AoNV were able to hold the line against a sequence of weak Union Generals, where, exactly, did the "strong" army of the south have any success? From 1861, the south was losing territory in large chunks to the Union armies in Kentucky, Missouri, Tennessee, western Virgina, New Mexico Territory, Mississippi, Louisiana, etc. And that is not to mention the stranglehold the north had on all of the southern ports-of-call.
The south was doomed from the very beginning, and "President Hannibal Hamlin" and an outraged North would have seen the war out to a similar conclusion.
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.