The low-frequency stability of a compact-torus ion-ring hybrid configuration, in which part of the toroidal current is carried by a ring of high-energy ions, is studied. In particular, the magnetohydrodynamic (MHD) tilt and radial shift instabilities in spheromak-like hybrid systems are considered. The ion ring has a stabilizing effect on the tilt mode, through its modification of the magnetic geometry. For the shift mode, the stabilization is dynamic for moderate elongation, but is again geometrical in the limit of large elongation. For moderate elongation, it is found that a high-energy ion component substantially enhances stability against the MHD shift mode.