I've heard the last foreign slave ship came to the US around 1815 but I've also heard that the slave ships were still coming durning the American Civil War.
While it was not statistically significant, illicit importation of African slaves did continue. At various points during the antebellum era the US stationed naval squadrons off the coast of western Africa to combat that illicit trade. That being said, the US, unlike the British, were never particularly enthusiastic about enforcement. Although international slave trading was a capital offense, no slave trader was actually hanged until Lincoln came into office.