i guess solenoid is an inductor (L), R2 and C1 forms resonant circuit, hence oscillation. from the original circuit in OP, try adding capacitor (maybe 0.1uF) from 9V to input trigger, and resistor (maybe 1Kohm) from input trigger to ground. reduce R1 to say 1Kohm or 100 ohm. during startup, the capacitor should momentarily giving initiating pulse to turn the thing ON and applying trigger LO later on to deactivate relay (OFF state). it may work it may not depending on the leakage. and maybe also reduce R4 to between 1-10Kohm. ymmv.