It's not clear what you want to do but if you generate a rectangular wave with the on/off cycle you want, you can use it to trigger a gate that controls a solenoid. Or two gates of opposite polarity to cause one or the other solenoid driver to activate.
Simpler would be to drive a PNP and an NPN power transistor, each driving its solenoid. Your only concern is adequate drive as well as suppression of inductive spike on turn off (diode).
The PNP will activate when its base is pulled down, and the NPN when its base is pulled up. If you want to drive a solenoid with a higher voltage you will need another transistor in each drive circuit.
If you only want to drive one solenoid you can omit either of the power transistors.