I am looking for a good way to lose weight, but unable to exercise very hard?

I have been diagnosed with Hyperthropic Cardiomyaopathy with Mitral Valve Prolapse. I am part of a Cardiac Rehab exercise group but only allowed to get my heart rate up 20 to 30 beats higher than resting (80-90 higher). I am not losing any weight. Need a good diet plan.