I read something about this years ago and remember that they suspected it had to do with narcolepsy. Read about that issue, as I think I had the problem and stopped using coffee to stimulate my sleepiness. I also exercised more by walking a couple of miles. I never had shaking, however. It may be associated with low blood sugar because when the numbers get too low, you shake and want to pass out.
When I was in that condition, I drank milk and ate a snack and the blood sugar recovered. I ate six times a day. But I always found it was not helpful to stimulate with coffee or chocolate. I only drank one cup of coffee in the morning for many years. Finally I gave it up because of gall bladder problems and had my gall bladder removed due to many "seeds" they called them. I never went back to coffee.
Coffee aids the bowel movements, so after that I ate dates which made my mornings better. I recommend dried fruit for that problem.
Sometimes it is a matter of tweeking the digestive system and coaxing the body to work more efficiently. Diabetes is a problem where the body in some places does not do its job well. Type one is when a body part quits working altogether so insulin is needed. Dorisena