How can I fix a "singing" capacitor
This effect that you mention can be caused by an electrical or mechanical disturbance. If the effect were mechanical you would see that the vibrations are causing an analog resonance within the capacitor which sends a signal somewhere. You see this a lot in small PCBs made for wearable devices. This electrical variant is different in that the circuit is creating the resonance, but the fact remains that this resonance can be killed.

For a lower rated capacitor I would say just throw in a tantalum, but since this is a high voltage capacitor you will have to keep the ceramic and add something else. A ferrite bead is possible. The added resistance will create a damping effect. You need to be careful with this, however, that you don't drop too much voltage when adding line resistance. Decoupling caps are likely the way to go, however. Without looking at the circuit I can not say for sure, but they will probably stand up to any spikes.

You touched on this in your question. Either put two in parallel that add up to the same value as the original, or you can actually add a separate path to ground through a decoupling capacitor. Again, without looking, I can not tell you exactly, but if this interests you just look up decoupling caps and your answer will find you. Hope this helps.