Measure the resistance “R” of the two relay coil terminals (ohms).
Excite your coil with AC of frequency “f” 50 or 60 HZ. Increase gradually the voltage not to exceed the full load current.
Measure the voltage applied “V” (volts) and the current “I” (amps), calculate the impedance “Z”.
Z = V/I
Now calculate the inductive reactance “Xl” .
Xl = SQRT (Z^2 – R^2)
Calculate the inductance “L” (henrys)
L = Xl / ( 2*PI*f)