Some large libraries, government websites, and archives have excellent collections of primary source material in many areas. These collections will have some primary sources related to African American history:
Library of Congress
Library of Congress Digital Collections
New York Public Library
NYPL Digital Gallery
Digital Schomberg (Schomburg Center for Research in Black Culture)
The following databases are available through NYPL but you must log in with your NYPL library card barcode and PIN:
National Archive (United States)
http://www.archives.gov/
National Archives (United Kingdom)
http://www.nationalarchives.gov.uk/
United Nations
http://www.un.org/