Prior to the Civil War, some slaves were buried in slave cemeteries or on the plantations of their owners (usually only if the enslaver recognized them as their children). After the Civil War and when African Americans were allowed to establish their own churches, cemeteries were also established. The exact methodology of who was buried in the cemetery varies by location.
For the most part, members of the church would buy family plots. Deeds were issued by the church and allowed members to waive their rights to the plot to give to a cousin or an Aunt who didn't have a final resting place.
Many churches have kept these older records of burials as well as memberships and sermons (if you have a relative who was a Preacher, you might want to look into the possibility of obtaining his sermons). Membership records are ideal sources of information because it can lead to clues as to other relatives who lived in the area, belonged to the church, who are buried in the cemetery as well as relatives living out of state.
Smaller churches in very rural areas might not have a church secretary or services every Sunday. Elders in the community usually have the names and phone numbers of the pastor, the secretary or a deacon of the church and will be happy to share the information with you. Obtaining tax records from the IRS might also be another option if you can't contact a knowledgeable person in the community. This is a FOIA (Freedom Of Information Act) process and could take some time to have the results returned to you. Larger churches are usually fully staffed with full-time personnel so your chances of a speedy result are greater.
If the church does not have the records you are looking for, you'll have to visit the cemetery itself and conduct your own investigation. Please refer to the cemeteries page for more information.