Did your vet. suggest eczema/feline acne-and wiping/washing off the area regularly? Allergies if you are giving her something new, or newly developed allergies? Lack of grooming-arthritis? Or if she is eating less she may be grooming less.
WEB MD has pictures of FELINE ACNE that may help. I (google) typed in black discharge on cats tail.
There were several references to "STUD TAIL" which may be quite helpful if you research that topic. You may want to confer with your vet. FIRST before following any suggestions-she may have ruled these out already with good reason.
Thank you for caring and working towards an answer!
#PetHealthandNutrition