A rechargable 9V battery has a better chance, but basically they are low current batteries, 50mA is going
to work, 100mA or more may be pushing it. Once overloaded 9V batteries rapidly drop to a few volts and
get warm.
However with a DC-DC converter dropping that 9V down to 5V you ought to get away with it as you won't
need nearly so much current at 9V - I'm guessing the thing will run from 5V directly?