Charge pump for stepping up 9V to 45V
A basic capacitive charge pump can only double the voltage, minus voltage drops in diodes.  You would need at least 3 stages of doubling.  Other types of charge pumps add the input voltage (again, minus a bit) to the output each stagle.  For such a charge pump you need at least 6 stages, since 45 is exactly 9 x 5, so 5 stages can't get there due to some inevitable loss.

So what's the solution?  A boost converter.  That uses a inductor to boost the voltage.  You say you don't want to use a inductor.  However, you provide no justification for that, so this is still a valid answer.  We are not here to indulge your religious hangups.

A flyback converter uses a transformer.  I don't know if such a beast falls into the catagory of evil inductors in your belief system.  The sacred scrolls can be interpreted either way.  In any case, a transformer-based power supply, whether in flyback or forward mode, can do this in a single stage, just like a inductor-based boost converter.