The cooling channel of the Muon Ionization Cooling Experiment (MICE) consists of eighteen superconducting solenoid coils, which are magnetically hooked together and contained in seven modules. The operations of a pair of MICE superconducting coupling magnets are affected directly by the other solenoid coils in the MICE channel. In order to meet the stringent requirement for the magnet center and axis azimuthal angle at 4.2 K, a self-centered tension-band cold mass support system with intermediate thermal interruption was applied for the MICE superconducting coupling magnet. The physical center of the magnet does not change as it is cooled down from 300 K to 4.2 K using this support system. This paper analyzed and calculated force loads on the coupling magnet under various operation modes of the MICE cooling channel. The performance parameters of a single-band cold mass support system were calculated also.