Here is one topic I'd like to see someone pursue.
In the last decade of the 19th century and the first decade of the 20th century, as many African-Americans moved to interstate within the South as moved to the North during the much more famous great migration of the 1910s. Yet there is very little written about this massive intrasouth migration. As with the later migration to the North, African-American migrants within the South were seeking economic opportunity and jurisdictions that granted them more security and rights. Surprisingly, for example, the Delta area of Mississippi, which had a severe labor shortage, was considered a haven for African-Americans through the mid-1890s.
A student who wanted to pursue a PhD thesis on this topic could choose one of several routes. First, an especially ambitious thesis would try to cover the entirety of this migration. Another option would be to focus on one aspect of this migration, such as the migration to the Mississippi Delta. My favorite option, for what it's worth, would be to focus on the activities of a man named Robert A. "Peg-Leg" Williams, a labor agent who claimed responsibility for moving up to 100,000 African-American migrants to Texas, Mississippi, and Louisiana. Williams was a very colorful character whose exploits frequently appear in local newspapers in the late 1890s. His labor agent business was eventually shut down by a series of state and local laws, leading to the obscure Supreme Court case of Williams v. Fears in 1900. As good a place as any to start looking into any of these ideas would be chapter 1 of my book Only One Place of Redress, which cites almost all of the extant literature circa 2000 on African-American migration within the South in the late 19th century. You can download the law review article that eventually evolved into that chapter here.