First you desolder the stick from the PSX controller (ps1 sticks are cheap plastic)
Then you solder it to a piece of PCB. (this is really kind of optional since the PCB dsont do anything really...)

Then cut a NES button in half and glue it on top of the stick. if you don't like the inversed button feel, use a SNES button.

Ta daaa! It is now a small version of the analog stick that will fit almost anywhere.
Mounting it is real easy, just drill a hole for it in the case, poke it through, and glue it in place.
NOTE: I did this a long time ago, and I have never actually used it in a portable. Just so ya know. I just though somebody might be able to use it.