Coffee is pretty acidic so if you suffer from heartburn or indigestion or have stomach ulcers then the black coffee or any other coffee can cause irritation of your stomach.
The acidity in the black coffee or other coffee can sometimes overtime irritate some peoples stomach lining which can then eventually lead to gastritis, heartburn and stomach ulcers especially if you drink the coffee on an empty stomach.
If you eat breakfast or something before drinking the black coffee then it should not cause any problems but even then the problems with hurting your stomach with the coffee happens slowly and gradually over years.
So it won't happen right away but if you notice that your stomach is hurting or you're getting ulcers or gastritis then you might want to avoid the coffee for awhile and then speak with your doctor about the health problems.