If you're talking about in-game prompts for any given PC game (i.e. "Press X to reload" in a call of duty game or something) they're specific to that game and chances are the only way to change them would be through in-game options if they even give you the option to change those. Re-mapping controller buttons is a common functionality, but changing the "type" of controller from xbox to playstation to mouse & keyboard isn't (not to mention the variety of controller styles for each system, different buttons, extra buttons like turbo, etc). The only game I've played that does this is Spelunky... if you're playing without a controller connected the prompts show up as keyboard commands, but if you plug in an xbox 360 controller the prompts appear as xbox buttons... I haven't tried it with a playstation controller though
If there are no options in-game the only other solution would be to have some sort of 3rd party utility that alters the actual game files, but it would need to vary from game to game... unfortunately all PC games don't have a "controls.cfg" file with code like "reloadPrompt = X.button"