Rotating machines are often subjected to fluctuating torques, leading to vibrations of the rotor and finally to premature fatigue and noise pollution. The automobile industry uses centrifugal pendulum vibration absorbers (CPVAs) to reduce the vibrations of the transmission system. These passive devices consist of several masses oscillating along a trajectory relative to the rotor. Previous studies showed that a CPVA configuration with two masses oscillating in phase-opposition and at half the excitation frequency is efficient in reducing the rotor's vibrations. In this work, former results on this subharmonic solution are extended to a new class of CPVA, whose particularity is that masses now admit a rotation motion relative to the rotor. To investigate the subharmonic behaviour of such systems, a dynamical model based on an analytic perturbation method is established. The aim is to predict analytically the subharmonic response, its stability, and to provide design guidelines. The validity of the model is confirmed through a comparison with a numerical resolution of the system's dynamics.