I think the courts should hand out punishment, because judges and juries have far more knowledge of the cases than any private citizen. You don't know how serious a crime might have been, you just know a name shows up on a list somewhere. You can make all the rules you want regarding private spaces, but it gets trickier in public ones because once a sentence is served and a person is released, they have rights to be in the same places as everyone else. Because 'everyone else' is in no position to take a person's rights away.

What it comes down to is protecting the children. You can make a library less of an opportunity. You can make it possible to see what's going on everywhere or make it appear as though you can. Videocameras or human eyes and a lack of secluded areas.
You can have people come in through one point where an employee can see and possibly greet them. Criminals are less likely to DO anything if someone's seen them and acknowledged them.
You can invite police who specialize in investigating child predators to come in and recommend practices and facility changes to make the place safer.

You may not only prevent known predators from hurting a child, but prevent the unknown ones from doing so. I believe prevention should be the focus and keeping convicted predators out would be more for show than for real, effective prevention. Looks good--may not work very well.