Yes, you can use two DC-output wall warts together to make a + and - supply.
Connect the - output of wall wart A to the + output of wall wart B. That point then becomes your ground (0V reference for everything else). The + output of wall wart A will then be the + supply, and the - output of wall wart B the - supply.
If these are 9 V regulated wall warts, then you don't need the 7809 and 7909 regulators. That would be simpler and the recommended arrangement.
If you do use a regulator, not that the negative one needs to be a negative regulator, not a 7809 as you say. A 7909 would work, and is the negative equivalent of the positive 7809. The unregulated voltages from the wall warts would also need to be a few volts past (higher for positive, lower for negative) what the regulators need. The 78xx and 79xx series require a few volts headroom. See the datasheet.
There is no need to use a separate supply for the DMM display. It should be able to run from the same +9 V supply as the amplifier.