If one side of the coil is connected to +24V you can sense the others side of the coil for voltage through a 47K resistor to th base of a transistor. Adding a diode and a 4.7uF capacitor can provide a hold in during pulsing. This will sense a missing counter or open coil.
Running a small current through the coil to make approximately 0.5 volt will allow you to sense an open or shorted coil with a high/low comparator.
Sensing coil kickback might also be a very quick cheap method of determining a functioning counter.