Drinking Coffee on an empty stomach can cause diarrhea in some people especially if they suffer from digestive issues or something such as gastritis.
It's okay to drink coffee on an empty stomach though as I do it myself while I'm fixing breakfast and I've never had diarrhea from the coffee when drank on an empty stomach.
Because Coffee Contains Caffeine "at least the caffeinated coffee" does and that Caffeine can cause gastrointestinal discomfort by increasing the production of your stomachs acid which can lead to diarrhea in some people.