OK, done away with the op-amps completely. Could have stuck to BJTs only but that would have required a high gain differential pair as the second amplifier needs to have a DC reference level and a large input impedance and so a MOSFET had to be used there. That now drives an emitter follower that pumps 3.2 V peak into an 8 ohm load, delivering peak pulses of 10/8 ~ 1.2 W every time the coil is pulsed.
The BC547 cannot handle a watt of power continuously but may survive here, depending on the pulse rate used as the mean power over time will be significantly lower. It if melts, swap it for a medium power type
. Should be loud enough for anyone without a hearing aid.
Had to modify the RC network values to suit the devices - see schematic.
Also raised the first amplifier's load to increase gain.
VR should now be 200 K Ohms

Output with VR set to 10 Ohms

Output with VR set to 130 K Ohms
The BC547 cannot handle a watt of power continuously but may survive here, depending on the pulse rate used as the mean power over time will be significantly lower. It if melts, swap it for a medium power type

Had to modify the RC network values to suit the devices - see schematic.
Also raised the first amplifier's load to increase gain.
VR should now be 200 K Ohms
Output with VR set to 10 Ohms
Output with VR set to 130 K Ohms