Actually skydiving is covered by part 119. It is listed as an exception to the Common-Carriage rules (that means you don't need an air operator certificate to conduct "intentional skydiving within a 25nm radius) and so you can advertise and run a business with no operating certificate.
Part 119.1 (e)
e) Except for operations when common carriage is not involved conducted with airplanes having a passenger-seat configuration of 20 seats or more, excluding any required crewmember seat, or a payload capacity of 6,000 pounds or more, this part does not apply to—
(1) Student instruction;
.......................
(6) Nonstop flights conducted within a 25-statute-mile radius of the airport of takeoff carrying persons or objects for the purpose of conducting intentional parachute operations.
This means that you can run a commercial skydiving operation and the pilot can be paid so long as he meets the requirements of part 61 and 91 to be a commercial pilot.