What you need is a variable frequency source and a sensitive DVM and a 1M resistor and a selection of capacitors to resonate the coil. . Connect the signal generator to the DVM with the 1M ohm resistor. Connect your coil to the DVM. Connect a suitable capacitor between the coil and earth. Twiddle the signal generator until the level on the DVM dips, this is the resonant frequency. with the value of C known, the frequency known, you can calculate the value of L.
A much less accurate way is to use a CRO's "cal out". If your CRO has one, connect a suitable capacitor across your coil and put them across the cal output. If you examine the wave form it will be a series of damped oscillations at the resonant frequency and then do the calculations. for more accuracy, feed the cal to the tuned circuit via a 100K resistor and use a 10:1 probe to reduce the stray capacity across the tuned circuit.
Frank