Is there any research showing that laptops cause harm/cancer to male or female reproductive organs?

Yes, indirectly. The male testes are situated outside the body cavity because they are designed to optimally function a few degrees below normal body temperature. Sources of heat like warm laptops and electric blankets if used excessively can decrease male fertility. There is inconclusive data on whether electromagnetic fields from laptops and cell phones causes direct damage to these organs.
Computers and Cancer. I am not aware of any. There are some studies that purported to show a connection between skin "burns" from the hot fans of laptops resting on the lap, but none that link superficial or, to address your question, internal cancers/harmful effects on the reproductive organs.