Here is a list of documentaries about Martin Luther King Jr.'s activism in the 50s and 60s:
King in the Wilderness -- (2018)
"I am MLK Jr." -- (2018)
"Bringing King to China" -- 2011
"The Witness - From the Balcony of Room 306" -- (2008)
"King: Man of Peace in a Time of War" -- (2006)
"The March" -- (2005)
"Dr. Martin Luther King Jr., A Historical Perspective" -- (1994)
"Eyes On The Prize" -- (PBS series from 1987 to 1990)
"In Remembrance of Martin" -- (1986)
"King: A Filmed Record; From Montgomery to Memphis" -- (1970)