I'm going to second what Knotted said- take soluble fiber supplements about twice a day in a modest amount. Metamusil is the somewhat expensive brand name of the psyllium grain husk soluble fiber. This type of fiber, as Knot said, tends to 'normalize' your bowels- in other words if you are too constipated it helps move things along gently, and if you have IBS with unpredictable diarrhea attacks, it really helps solidify and normalize that too.

Here's what I take, 2 capsules, twice a day:
http://www.allstarhealth.com/f/yerba...llium_husk.htm
It's the same thing as Metamusil but way cheaper. It's gentle and natural and simply helps normalize everything. It can help a LOT if you take a modest dose routinely.

Other than that, I'd say you ought to forget the coffee in the morning- it's obviously triggering a morning attack for you. You state you have a normal event when you get up and then a loose attack after your coffee.
Try some herbal tea (no caffiene) in the morning with a small amount of toast or something, along with a couple of fiber capsules. Take your fiber as well before going to bed, or with evening meal. I bet if you do this you will see a huge improvement.
Definitely avoid fruits or veggies with hard-to-digest skins- like tomato, peppers, apple skins, grapes, eggplant, and also mushrooms. Lettuce can be bad troublesome too.