We show that multiple sets of superconducting coils can be used to generate the magnetic field profile required in a synchrocyclotron, replacing the ferromagnetic pole pieces typically used in these machines. Coil number, location, and current are adjusted to produce the required field for particle acceleration. Superconducting coils are likewise used to magnetically shield the device, eliminating the need for a ferromagnetic return yoke or ferromagnetic shields. The results demonstrate several significant advantages for a design that eliminates the iron yoke and poles and relies instead on high performance superconducting coils for local field shaping and for magnetic shielding.