Using the output of a Pi pin to toggle a higher powered circuit
At these stated current and voltage, any common small signal transistor like the 2n2222 would work. 16 mA from your RPi at the base with a worst case hfe/gain for the 2222 means up to 450 mA at the collector. All you would need is a flyback protection diode on your coil to protect the transistor from the collapsing inductance field when you turn the transistor off. A 1n400x is okay for this application. It should be backwards across the coil.