It would probably be easier and less time consuming to get a chip that is supported by FVRSETUP.
That being said, the PICAXE 20X2 is based upon the PIC18F14K22 that does indeed have an internal voltage reference module. You should be able to use POKESFR to enable and set the FVR by writing to FVRCON register. You will then need to connect the ADC VREF+ internally to FVR, This is also done via POKESFR of the approrriate ADC register.
The registers to configure and their memory addresses can be found in the PIC18F14K22 Datasheet. POKESFR is explained in PICAXE Manual 2.
Good Luck
I downloaded the PIC18F14K22
data sheet but can't seem to find the actual addresses of the appropriate registers.
See posts #7 and #10. I believe that was a definitive conclusion that it cannot be done on a 20X2. Someone may want to re-test, check they get the same results as I did.This thread has some useful information but no one pursued the issue to a conclusion.
http://www.picaxeforum.co.uk/showthread.php?28380-20x2-and-FVR&highlight=adcon1
See posts #7 and #10. I believe that was a definitive conclusion that it cannot be done on a 20X2. Someone may want to re-test, check they get the same results as I did.