C2 is part of a low pass filter, and will stop any high frequencies going through with the default values you had. You don't need that, or it's resistor, add small capacitors across the feedback resistors.
Personally I think the specification is very poor - you're chasing 20Hz-20Khz - this is just the standard audio bandwidth, and not of any great consequence.
For a 'practical' design I wouldn't even consider calculating the coupling capacitors, just stick a value in that's 'more than large' enough, and perhaps a 'little' calculation on the feedback capacitors (which you don't seem to have) to roll off the HF somewhere above 20KHz.
If for any crazy reason you needed sharply defined filtering, then you'd usually do it in the filtering/tone control stages - but this was all in ancient history to remove rumble etc.