the hum/buzz on relays comes from wear on the coil top, dimples worn into the armature plate, or excessive spring tension (someone installed the wrong spring). Rarely it's an issue with the relay frame.
if the armature plate doesn't sit squarely on the coil top, it rocks/vibrates as the magnetic field in the coil fluctuates, especially as the voltage crosses zero.
if the plate has dimples what sometimes works is whacking it with a hammer on an anvil to flatten it out ... it's not possible on some plates due to attachments or the shape of the plate.
occasionally filing the coil top helps ... at least enough to remove any burrs from the edges of the metal pegs on the coil top.
the electrical tape is the easy fix to just damp the vibration. If it's still too loud, then yup, it's ok to disable the coil and zip tie the armature plate down. It's not likely you'll have a hopper coin overflow/overfull issue in home use.