Is there an app that can set time limits for Internet access?
Don't overlook "the parent app".

It turns on the logging of safari using parental controls. Sets the normal time limits when the mac can be on and off.

Then it communicates to the children "the rules" and what happens when the parent determines that they have been broken. Why spend money or time on a more controlling solution if you can ensure they don't cover their tracks and will be caught if they stray.



Technically, managing this on the router is easier than on the Mac using the default Apple tools. 

Apple has implemented timed access across the airport line, so fire up Airport Utility and set the times when you want access to the Internet. 

You can set up default timed rules as well as specific policies for specific devices. 

If you really want things to be controlled locally on the OS, turn on time limits under Parental Control under system preferences for each user account:



And then prevent apps that you don't explicitly want them to use.



I believe Firefox (if installed) defaults to on - so do review each and every app in the list. Your children can come to you as the administrator and you can over-rule these restrictions with your password - so this is the unattended default situation and you can grant them extra leeway with your password when needed.