As the time period you mention is from the Missouri Compromise to the beginning of Civil War, slavery was legal in half the country or more for that entire span of time. With 4 million African-Americans still legally owned by 1861, there were tragically few elements of their society that can be called "institutions". Your instructor may have a definition he wants you to work within, but lets start with two that survived two and a half centuries of slavery: Marriage and Religion.
Marriage between free blacks in various parts of the country endured just as it did for the rest of society (albeit still with overt and abundant racial discrimination), but slave marriages had no legal status whatsoever. Either person could be sold into slavery in some distant place, and then slaves often married again. This meant family boundaries were somewhat fluid, and relationships more temporary and tenuous.
New Testament Christianity thrived and spread among the free black community during those years, and to plantations as the message slaves found within the Gospels gave them hope that someday they would be liberated, and that a just God would save them from slavery. The roots of this distinctly southern African-American religion formed the basis of the Christian-backed movement that would lead the calls for civil rights in the mid-20th century.