A very rich and upright businessman has been diagnosed with a disease that requires an organ transplant. He now considers buying an organ from the black market and is under pressure to cut corners to survive.

I like the possibilities here. I assume the story is not about him 'considering' finding a black market organ, it's about him actually pursuing it (whether or not he does it in the end):

A rich, upright businessman is?diagnosed with a life-threatening disease, and must enter the shady and dangerous criminal underground to find the black market organ that will save his life.

I don't think it's necessary to specify the organ, only in that "black market organ" is a pretty common term, vs. saying something like "black market pancreas". Or maybe that's actually fine too.

Is there a specific antagonist? Perhaps someone who wants him dead in order to take over his company, inherit his wealth, or something like that? That would help round out things.

I think it would help if the logline specified the organ. ?Heart? Kidney? ?Liver??Lungs??Pancreas?

I think it would help if the logline specified the organ. ?Heart? Kidney? ?Liver??Lungs??Pancreas?