Previously, hybrid simulation techniques using massless fluid electrons and kinetic ions have been successfully applied to study the electromagnetic plasma waves generated by ion pickup in the solar wind, where instability is driven by the large drift velocities of newborn ion populations. For ion pickup at Jupiter and Saturn's magnetospheres where instability is driven by heavy ions with a ring velocity distribution, we show that the one-dimensional hybrid simulation technique can successfully reproduce the behavior of this instability as predicted by linear dispersion theory as well as the important nonlinear wave-particle interactions. The simulated ion cyclotron waves have frequencies near the ion gyrofrequency and are generated as the anisotropic newborn ion ring distribution scatters to a more isotropic configuration. Simulated maximum wave amplitudes and instability growth rates increase with newborn ion density and pickup velocity. For appropriate heavy pickup ion densities and velocities the simulated wave amplitudes are within the range observed by spacecraft.