If time capsule can not be set up to log the web sites that users access, is there third-party software that will accomplish this for time capsule? Ideally something that would work through the time capsule and not have to be installed on each individual device, but would allow analysis by device.
The router itself does have DNS caching, but that cannot be accessed without rooting the device (and probably changing a few settings that shouldn't be changed to do logging to disk). Furthermore, an automatic update may reset everything, so I wouldn't go down that path at all. Much better idea would be to set up a DNS on a small linux machine and then configure the Airport DHCP to use your small Linux computer's DNS server as the default. That will persist through updates, etc. All clients connecting will ask the linux machine for the IP address of the website they want to go to. Just log it.
Also, for what it's worth, even if this is your network and these sorts of invasions of privacy are easy to do, I really really REALLY recommend you make everyone (children, etc) aware that this logging is going on. For everyone's sake.