Stats of black Head Coaches in the NFL since 2000, from
Deadspin.
With few exceptions (Flores (Dolphins); Lovie Smith (Bears); Jim Caldwell (Lions)), all had losing records overall, and most firings came after an exceptionally poor season, or series of poor seasons. Of course, firing for these reasons seems to be universally applicable - regardless of color.
It's interesting to note just how poorly most of the successors performed. The vast majority of them were fired as well after one or a handful of seasons).