I would like to stay here for two nights. Friday night is available but Saturday is booked. If I stay on Friday what is the chance I can get a campsite for Saturday by picking up on a “no show”?

Call the park ranger directly and they can tell you how often no show sites become available. Also, some sites are not part of on line booking and must be reserved via phone call to the park.

you could always drive to Bastrop State Park and try there too. they are connected by a park road that's a pretty nice drive