Caffeine has a stimulating effect on the bowel muscles. This effect can either help to regulate bowel movements for people with chronic constipation or cause havoc for those with a sensitive intestine.
In general, the stimulating effect is transient and not expected to result in any long term damage or injury to the digestive tract. For people with fatty liver, drinking 2 cups of coffee daily may even have a desirable effect on the condition.
Do listen to your body and watch out for unwanted side effects of caffeinated drinks on your body. If you experience discomfort repeatedly with such drinks, the best is to avoid them altogether. Otherwise, enjoy your drinks!