Going off guaranteed specs (not typical behavior), you're going to have a hard time I think. You could make a current limiter out of a transistor (pair end-to-end, or single inside a FWB), so it works for AC, use the 120V coil, and have it limit the current just beyond what's normal. The excess is dissipated as heat.
It would be nice to have a nonlinear component (inductor or capacitor) that can do this naturally; the coil itself might work (most likely has a laminated iron core), but it's hard to say as the inductance probably isn't well controlled (and who knows if the manufacturer decides to modify the design later). The operational idea would be something like a ferroresonant transformer (supply the coil with a capacitor, such that the resonant frequency is near line frequency; as the core saturates, resonant frequency rises and amplitude -- and current draw -- levels off). Pull-in might even be hampered with such an approach, because coil inductance varies with operating state (it's very low initially), so the tuning would be all off. There may be no single approach that works real well here.
To me, this doesn't sound like a common "electrical control" problem, the kind of thing where you'd use relays -- if you could tell more about the application, maybe something better could be suggested.
Tim