"Coach, if he runs, it's as a pinch runner. He can't courtesy run there since he's already run for the catcher."

I have no intention of coaching a coach, all I'm doing is stating a fact after he's run a runner out there. It's his decision at that point.

Not an illegal sub unless he had CR earlier in the inning. When he takes the position of a runner he becomes a substitute and not a CR since he was not eligible. He is now in the game legally and they will have to use the re-entry rule if they don't want to keep him in.

Incorrect.

Once the coach says, "courtesy runner for the pitcher," you cannot simply make this player an unannounced sub. Disallow the CR and, if you like, clarify that the sub may enter the game only as a pinch runner (and will subsequently be ineligible to serve as a CR again).