I don't know the combination of controls you have to press to replenish the stamina of your Chocobo (I don't even know if it's cheat, bug or intended feature for that matter), but the point is that you just press the same combination on PSP as you would have press if you played on your TV console.

The only problem might be that PSP is two shoulder buttons short when compared to TV console controllers. To overcome this problem, just open the PSX emulator settings on your PSP a check (or edit) the controls mapping (press Home and choose Controller settings or something like that). Hope this helps.