Your challenge is to have with a POD of after Washington's inaguration to have at least one coup in the United States. Bonus if a true civil war (ie for the control of the whole government and country) happens.
The Coup of 1813...On June 19, 1813, anti-war Federalists from New England, fed up with the destruction of their economy first by Jefferson's Embargo and now with Madison's War, decide enough is enough. With assistance from the British Navy, the Federalists land a force which takes Washington, D.C. and captures President Madison and most of Congress. George Cabot of Massachusetts is named President of a Provisional Government. Meanwhile, Vice President Elbridge Gerry and those members of the Congress which escaped the Federalist attack set up a rump government at Philadelphia. Several New England States call up their militias to support the Federalist government, while volunteer regiments from a number of States currently serving with the United States Army against the British defect to the enemy lines, and are repatriated to support the coup as well.
The legitimate government in Philadelphia raises forces of it's own, primarily from the Southern and Western States, which are very hawkish and view the Federalist coup as treason, pure and simple. A 3 sided war (United States Government versus Provisional (Coup) Government and the British) results, which initially goes very badly for the U.S. Government. The U.S. Government under Gerry is soon forced to make peace with Britain in order to deal with the Provisionals, as they come to be called. In a humiliating treaty, much of Northern Maine, as well as parts of Michigan, are surrendered to the British in exchange for peace. The ceding of northern Maine proves to be a masterstroke for the U.S. government, as Maine is still part of Massachusetts at this time, and Massachusetts is one of the prime supporters of the Provisional Government. This puts the British into conflict with the Provisionals, and the British withdraw even clandestine support for them.
By early 1815, the U.S. has gained the upper hand in the war, and U.S. troops march into Washington on June 1, 1815. The Federalist Provisional government flee abroad, and their dispirited forces surrender. The war is over by the end of June.