How to determine what capacitance is required for eliminating humming noise?
Any cap above 670uF would do their job, like 1000uF, and also remember to use always a higher rated voltage, like 16V in this case.

I calculated it in this way: With 0.3A and 9V power consumption we can treat your device like an equivalent resistance of 30 Ohms. Like in RC low-pass filters, we could determine their filtering frequency using 4 times tau to get away any 50 Hz or other harmonic of your mains frequency.

This is 4*tau=4*R*C -> 0.08=4*30*C -> C = 667uF

I always have in my toolbox a pair of handy 2200 uF 16V in case I need it :)