Rechargable 9-volt batteries will not work because they are not truly 9 volt batteries! The dirty little secret is that they are actually 7.2 volts due to the fact that there are 6 tiny 1.2 cells inside making up the 7.2 (bet you didn't know that - they are a rip!). So it starts out at 1.8 volts from 9V, and that is not even going under load yet. Our basses need at least 8.3 volts under load to work properly.
Any alkaline 9V will work, but it is best to stick to one brand, whatever it is. The reason for that is because the batteries may be of equal voltage, but they are not all equal length. A slightly longer 9V will push the copper contacts in the battery box in too far, then another, slightly shorter battery will not quite make contact with the tabs. You can correct this by bending the copper contacts back out with a jeweler's type screwdriver, but this is the last thing you want to worry about during a gig.
Lithium 9V batteries seem like a great idea, as they are supposed to last 3-5 times longer than alkalines. The problem is most of them do not fit in the battery box, they are too big.
Quirky things, these 9 volts.
Dan