The stability of kink modes in a cylindrical plasma column under the influence of an oscillating magnetic field applied in the azimuthal direction is studied. The frequency of the applied field is chosen close to the ion-acoustic frequency. It is found that coupling to damped ion-acoustic waves induces a small real frequency to the kink modes which can significantly affect their growth rates. Conditions for parametrically suppressing (or exciting) these modified kink modes are specified.