While it is not uncommon for some patients who have been smokers to experience some problems with their bowels after cessation of smoking, it is not common to pass black stools. If your stools are very black, almost like hot asphalt, there is a possibility that you may be passing altered blood from your gastrointestinal system, in which case, I would advise you to consult a gastroenterologist for an endoscopy to exclude an ulcer.
If, however, the colour of your stools is only slightly altered and is darker than usual, I would advise you to wait and watch for a couple of weeks since things may settle down in this period of time.