How did African-American institutions fare between 1820 and 1861?

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.