black stools are a matter of concern. Normally diverticulosis means presence of these small pouch like areas of the colon but these areas when get inflamed or infected can lead to mild fever, diarrhoea like state. further if these infected areas give away that means get perforated things can become a little more complicated that is bleeding can occur which may manifest outside as black stools.now what you need to do is take him to a hospital and get the scans done and check if any such perforation has happened after consulting your physician