It sounds like you have typical healthy bowel movement habits. In fact the majority of people that have regular bowel movements have them in the morning. The reason that you have them after your morning coffee is because of the caffeine in the coffee. Caffeine is a large bowel stimulant that increases the movement of your large bowel. This moves stool closer to your rectum which gives you the sensation that you need to have a bowel movement. This type of response also occurs in the morning after having breakfast. Eating stimulates your stomach which sends a signal to your large bowel telling it to move things out.
Because caffeine does increase your bowel motility, you should stop drinking coffee if you ever develop diarrhea. My patients with chronic diarrhea usually get worse with coffee. If you feel that this does not describe you, then you are probably fine. If you are at all worried about your bowel movement pattern, then you should schedule an appointment with your primary care physician
or internal medicine doctor
). He or she can take a more detailed history of your bowel movements and determine if there is anything abnormal. I think your doctor will most likely tell you that everything is okay.