We recently found the answer when our newspaper database vendor offered to send us a digital sample of our local newspaper. We asked for the years 1963 and 1964 because it was a time period that we needed for civil rights research.
As an obituary experiment I searched for a local funeral home in 1963 called Leevy's. I wanted to see if any obits would pop up. Nothing! Not a single obit in 1963 was published for African Americans. There were plenty of classifieds for Leevy's Funeral Home but not obits that would indicate Leevy's was handling the arrangements. I repeated the search in 1964 and suddenly, as though a water spigot was opened, there were obits. Take a look at the image below and you will see several classified listings for the Leevy's Funeral Home and then on October 9, 1964 the first obit is published. There are not alot of obits but they are definitely being published. (We still had a black newspaper until 1967ish and that was probably the publishing venue of choice. Unfortunately no issues of that newspaper remain after 1957.)
One of my volunteers who is very knowledgeable about the civil rights era hypothesized that it was the Civil Rights Act of 1964 that allowed the publication of African American obituaries. It makes very good sense to me so I am going to use that as my answer and it may also be the answer to other southern newspapers that you may be using for research.
Note to self: when trying to figure out why some trend is occuring check major historical events!