It may be possible with an LFO. But it certainly won't be easy. It might not even fit in the pedal.
Honestly I cant stand having too rock the pedal back and forth.I dont want to buy a new pedal though.
I seriously doubt that is something you would want to even consider researching...

How an Autowah and a regular wah pedal work are entirely different.

Just look into buying one.
Washburn D-12
Ibanez RG
Ibanez RG 7321
Epiphone Les Paul / EMG 81 85
Fender MIM Ash Stratocaster
Digitech Whammy
Small Stone Phaser
Boss SD-1-Modded
Boss MT-2-Modded
Boss CE-5
Boss DD-3-Modded
ISP Decimator
B-52 AT-212
sell your wah pedal, and buy a autowah pedal.
i know zvex and moog make some bad ass autowahs, but they are pricey of course.
There are lots of auto wahs available. Digitech Synth Wah is a decent, affordable option.