Though it was a rough several years after the end of the Civil War for the United States, we managed to stabilize ourselves relatively quickly. Just five short years later, the Confederated United States dissolved once Georgia was accepted into the Union on July 15, 1870. Furthermore, the 15th Amendment was ratified on March 30, 1870, thus allowing African-American men the right to vote. This amendment passed in time for the first elections of the year and many former slaves attempted to vote. Despite ratification, however, many protested the 15th and federal troops were called to major cities, including Philadelphia, to protect African-American Voters. Also happening in Philadelphia at this time, a mass emigration of Chinese immigrants from the west created the need for a Chinatown in Philadelphia; this mass emigration was caused by frequent race based attacks.
As for the two-cent coin, its uselessness became even more apparent in 1870 as its mint numbers came in below the one million mark because regular coin circulation had regulated by this time after the war. Still, this coin managed to prevail for another two years despite plummeting demand.