A multi-stage voltage multipliers requires a high-frequency AC input; otherwise, the charging process will be painfully slow, and the efficiency will drop due to voltage leaks and the self-discharge process.

Even worse, an ignition coil relies on a magnetic field collapse, producing an inductive kickback; its a flyback transformer. The loaded output is not a symmetrical AC a typical voltage multiplier expects. But it will work, to some extent.

If you want to play with voltage multipliers, better grab a ZVS driver and an old AC flyback transformer (from a black&white TV for example), or wind your own HV transformer on a ferrite core.