If you use a buck regulator, the inductance of the coil itself will mean you don't need a separate inductor.
If you use something like an LM2576HV-ADJ, with an output load of an 8.2 Ω resistor, and have the relay coil in place of the inductor.
The LM2576HV-ADJ will control the voltage on its feedback pin to 1.23 V, so there will be 150 mA flowing in the load. All the load current comes through the inductor, so its average current will be 150 mA as well.
If you do that, you must not put any capacitors or diodes in parallel with the coil, and it's a good idea to have the coil close to the buck regulator. The resistor will generate a bit under 0.2 W of heat, so a 1/2 W or more resistor would be best.
The circuit diagram is on page 12 of
https://www.ti.com/lit/ds/symlink/lm2576.pdf with L1 as the relay coil and "Load" the the 8.2 Ω resistor.