OK.. I'll hesitantly venture into this one.
Does the unit have a 3 prong plug? If it does, there is probably something "amiss" inside the coffee maker that is causing the GFCI to trip. Not necessarily life threatening, as heater elements frequently (with wear) have a slight trickle current to ground that could cause a GFCI to fault.
If the unit only has a 2 prong plug, and is tripping a GFCI, that is a whole different story. Don't have a good explanation for that, but would hesitate to use it until the reason is sorted out.
Good luck!