Depending on your definition of sniping you could place it as early as the American Rebellion - units equipped with rifled guns were used to shoot important folks in the enemy formations (officers, artillerymen, etc). The British took this practice into the Napoleonic war (hands up who has read Sharpe) and both sides employed it in the war of 1812.
Since smokepole marksmen were mentioned: The Lone Marksman BTW, just reeived John Walter's Voices of Snipers which covers WW I & WW 2.
American rifleman Timothy Murphy famously killed (strictly speaking mortally wounded) British general Simon Fraser in one of the battles of the Saratoga campaign.