The Civil War wasn't really a coup because the South wasn't trying to take over Washington D.C. or run the Federal government. A coup is usually a quick, behind the scenes power grab by a small group of people trying to unseat a leader. What happened in the 1860s was the exact opposite: it was a massive, public breakup where entire states voted to leave.

the post war assassination of Lincoln was, in a tiny sense, a delusion of coup, perhaps.