Why not just modify the one you have? Most of what you need is already there in your headphone amplifier.
The CMoy is a (very simple) amplifier built from a readily available schematic.
The amplifier itself looks like this:
The power section looks like this:
It is intended to drive a headphone from a line level source.
You are connecting two electret microphones to it.
Electret microphones require a DC bias voltage to operate.
They will also likely require some amplification.
The existing amplifier can easily be modified to provide both of those things.
Bias for the microphones:
Connect a resistor from switched 9V to each of the inputs (the point marked IN from the amplifier section and the point marked 2 in the power section.)
You will need two resistors (one for each channel.)
I would start with a value of 1.2k ohms.
The value isn't terribly critical. Anything from 1k to 10k ought to work. I wouldn't go below 1k - too much current might damage the amplifier in the microphone. Above 10k and you might start picking up more noise. Between those values you might see some difference in frequency response - I couldn't begin to guess which way, though.
Try that, and maybe crank the volume of the amplifier up to full.
If that works, you are done
If you can hear a bit from the microphones, but it is not loud enough, then you can boost the amplification.
R4 and R3 set the amount of amplification (the gain.) The gain is R4/R3. The values given in the schematic make a gain of 10.
If you change R4 from 10k to 100k, you will raise the gain by a factor of 10. That makes the gain 100.
Remember that you have to do this twice as well - once for each channel.
That ought to more than make up for the weaker signal from the microphones
I have ignored R5 from the schematic - it probably isn't there.
I have also assumed that the microphones are wired to the stereo plug the same way a line level signal would be. It is possible it is wired differently, but I don't see why anyone would