Mosfet push pull not driving inductive load as expected
If you are trying to use the FETs as a source follower current buffer for the Opamp, the sources of the FETs need to be connected to each other and the coil. 

The IRF9510 is upside down as drawn in your schematic.  That would allow current to flow through the coil (or N FET if it is turned on) and through the body diode of the P FET.  This will happen no matter what the state of the gate of the P FET is.  

After you correct the orientation of the IRF9510 the circuit should be able to apply about +/-11V across the coil.  Gate to source threshold voltage of these FETs is about 4V, so that will limit the voltage range of the source to 4V less than the bias voltage.  Also, since the two gates are tied together there will be a large area for crossover distortion between conduction of the IRF510 and the IRF9510, which may or may not be a problem for you.  

Edit:  Also just noticed that the ground reference at the batteries in the schematic must be wrong.  Ground should be at the battery +/- common point to get +/-15V.