Have a look at the attachment.
I am assuming that the original circuit was as I have shown, and that the line which I have called Return connects to the vehicle battery negative terminal (eventually).
I suggest that you add a diode and a capacitor to your relay as shown in my suggested circuit.
The diode can be a 1N4007 although any of the 1N400x series will be OK.
The capacitor is open to a bit of experiment, I would try something around 10uF to start with.
If the relay still buzzes alarmingly, try increasing the capacitor to 100 or 200uF. The larger capacitance would not hurt, but there may be a bit of delay before the relay de-energises.
JimB