The diode increases the current... i really cant see this doing anything but increasing the problem.
You do need to make sure that the coil is housed properly, if its loose then when it activates, its vibrates at 50hz and causes buzzing... the dark red tap washers that you get from Bunnings make good packers for loose housings... or you could fix the housing of course.

Clay has another cause which could also cause this..

3c. When Thing Still Don't Work: Buzzing/Noisy Relays and Coils.
In most EM games there are momentary and hold style relays. Momentary relays activate (energize) for just a moment. Hold relays activate for long periods of time. Examples of hold relays include feature relays (that keep a set of lights or features activated on a pinball playfield). The "hold" relay on a Gottlieb game (which is energized the entire time the game is turned on). Bally also has a "hold/lock" relay that activates at power-on after the left flipper button is pressed.
Hold and Lock relays are designed to be activated for a long period of time, without burning. In order to do this, the hold relay's coil will have high resistance (compared to a momentary relay). It should have 30 to 150 ohms. The higher the resistance the better (but the higher the resistance the less "pull" the relay will have).

Hold relays, because they are energized for long periods of time, can be noisy. This buzzing is caused usually by one thing: the spring resistance of the relay is too high. Either the relay spring is too short/tight, or the relay's switch blades are adjusted to provided too much spring resistance. If a relay has to really work to pull in its activator plate, the AC 60 cycle hum will result while the relay is "holding". The AC 60 cycles sets up a vibration which causes the noise. AC means "alternating current", as the voltage goes from 30 volts, to 0 volts, to 30 volts again and again, 60 times a second. As the relay goes to 0 volts, the armature on the relay can release slightly, and then the voltage goes back to 30 volts pulling it back. This often causes the buzz or hum.

Take a DMM and measure the resistance of the hold relay coil. It should be in the 30 to 150 ohm range. If there is the same relay coil number used elsewhere in the game, compare the two resistances, as they should be the same. If the suspect coil's resistance is lower, replace it.

With time, hold relays can get warm (hot), and burn the insulation off adjacent windings. This will lower the overall resistance of the coil. Then the coil gets hotter due to lower resistance, and the cycle continues until the coil burns crispy and brown.

Assuming the relay's coil has proper resistance and is not burnt, there are a couple things that can be done to minimize the buzz/hum. Adjust the relay with as little spring resistance as possible to pull in the armature plate. This will minimize the noise. Adjust the relay's switch blades and lengthen the spring so only the minimal amount of tension is needed to return the armature plate back to it's resting position. Even the contact surface between the relay coil and the activator plate can be filed to smooth it if it has wear. (Or just replace the activator plate and/or relay.)

On Williams games there is a brass rivet on the activator plate. Sometimes this rivet is missing. This can also cause the hum. Or the rivet can become loose and that can contribute to the noise, though this is rare (usually the relay is just adjusted too "tight", causing the hum).

Another hold style coil (though not a relay) are the flipper coils. If the player holds in a flipper button and the coils make a loud buzz, this can be often be fixed by replacing the coil stop. The coil stops on EM coils are slightly magnetic. This minimized the problem with the 60 cycles per second AC vibration.