The power supply of a Fast Field Cycling Nuclear Magnetic Resonance apparatus is typically a current power source, with characteristics that are not fulfilled by most of the commercially available power supplies. This current source is used to supply a specially designed magnet, and should be able to drive a cycling current with a slew rate lower than 3 A/ms. In this paper, two solutions for this current source are designed and discussed. The first uses two power supplies: the main voltage source and an auxiliary power supply to guarantee the current transitions from the low level to the high level. In the second solution the auxiliary power supply is replaced by a capacitor. To guarantee the required current slew rates, the possibility of using resistors to dissipate the energy stored in the magnet is also discussed.