@GaryTheSnail 

HomeCare routers are more limited these days.  All of our routers that would have had HomeCare now ship with HomeShield. Niether HomeCare or HomeShield have parental controls this precise.  In HomeShield Pro you can set "off-line times" and "Time Limts"  but the web filters are based on the overall settings of the profile and the devices linked to that profile.  We do not have tools that allow only specific website and specific times.    

  @GaryTheSnail 

HomeCare was provided by TrendMicro

HomeShield is a newer service provided by Avira/Norton

No currently there are no routers that allow the limiting of websites at specific times.  the main reason is that a device can only be linked to one profile at at time and the filters apply for as long as that profile is active.  

  @GaryTheSnail 

It would be more than just a schedule, at least for TP-Link and HomeShield.  You can do multiple schedules with our stuff now, it just pertains around online hours, offline times and bedtimes.  For how our controls work you would also need to be able to set custom filters for specific times as well.  We are happy to send it up but I just don't know how possible it is.  As was with HomeCare and TrendMirco wtih Avira/Norton's HomeShield each packet is inspected as it leaves and enters the router through their servers if its found to be not allowed the packet is blocked from entering or dropped and never arrives.  I don't know if the service can allow for a single profile to have varied filters based on the time of day.  Still we will send it up for review.  

  @GaryTheSnail 

Homeshield does that.  Customers can set "Time Limits" which allows them only X ammount of time online each day.  This is split between the devices on their profile.  So if a profile has 4 devices and only 6 hours of online time that would be collective between all 4 devices.  

Customers can set "Offline Times"  which shuts off internet service to all devices in that profile for that specificed time. An Example would be shutting all device access off during Dinner time.  

You can also set "BedTime" which is similar to Offline Time, but can go into the next day.  These can even be set at different times for weekdays and weekends.  

Some of these options due requre HomeShield Pro though. 

So settings sechedules isn't the issue.  Its setting filters that only apply to specific times. And while it might sound easy, Its more difficult than it seems, especially since it involves a 3rd party and how traffic is filtered through their servers.  I am not saying its not possible just It requires review to see if it can be implemented. 

  @GaryTheSnail 

Of course its my pleasure.  I just want to make sure the features are well known.  Its likley that they are handling the filters locally on the router itself. But it could also be that the feature was built specifically for that purpose.  To be honest this is the first time i have seen this request, at least as well described as this, so it could be that we just didn't think of it.  We will get it up to development and see what they say.  I will say don't expect a response though, at least not in the sort term.  We rarely get an update on requests and implementations until they start releasing in the firmware.  I can say though in the US updates are typically posted every Friday, because i am the one who posts them.  As long as there are no holidays or PTO by 4pm you can check if an update has been added to the website for your product.