Two 300RPM 12V DC motors connected to arduino motor shield r3 power supply

You have told us nothing about the motors that's useful other than they are 12V.

We need to know the stall current rating, and preferably the full rated load current/power
too. Any information please, even a photo would help to see how big they are.

If they are 12V why are you thinking of using 9V at all?

Small 9V batteries cannot power motors or servos, they just cannot produce
enough current, give up on the 9V battery notion completely!