Can anyone recommend a simple complementary pair amplifier schematic for this application.
Hopefully using BD139/BD140 which I have to hand.
And sound quality is not a particular issue - it doesn't matter if there is a little distortion going on.
Simplicity of schematic is more important than sound quality.
The 555 output is beefy and doesn't usually need amplification to drive a small speaker. You will need
beefy decoupling on the 555's power rails though, 1000uF or more would be wise.
If you need lots of watts, by far the simplest approach is an IC amp, so many to choose from, analog
or class-D. You'll need to ac-couple the 555 output, and probably attenuate it.
However if you stick with the two transistors, just use the standard class-B circuit, no need to bias for a
square-wave, so its pretty simple, but you'll need a large output capacitor.