If saying, "no," isn't an option, try these suggestions.
One option might be to set up a laptop with some sort of reversion/reimaging software. If you're into Windows, try something like DeepFreeze. This is probably the least labor-intensive option. You just need to un-freeze it, in a clean state, to do software and OS updates before re-freezing it again. The user has full control over the computer (as much as you want, anyway) and is simply reset to the pre-defined state upon reboot. The DeepFreeze software, I believe, can also leave some areas unlocked so changes there can persist through a reboot, if desired.
Another option might be to set up a laptop to PXE boot and get a read-only image to boot from. Configure all changes to be saved to local media until you decide to wipe it clean. This requires some network infrastructure to set up as well as keeping the custom boot image up-to-date.
Yet another option would be offer up an "unlocked" laptop but drop it on a "protected" VLAN with heavy internet filtering. Again, there's some network infrastructure to set up as well as some likely subscription fees for filtering software/hardware at the gateway. The bonus here is that, if you have any (now or later), kids' computers can be placed on that VLAN without too much worry on your part. It also protects the rest of your computer equipment from being attached from the inside of your LAN by a compromised device since it'll be on a totally separate "untrusted" VLAN. This isn't exclusive to the other options presented here, either, and can be used in combination.
You could also just bite the bullet and simply re-image the laptop every time someone uses it. Again, if you're into Windows, you could easily set up Windows Server with WDS and capture a customized WIM image so it'll have all the apps you want installed from the get-go. Other options exist for Linux and Mac.
One last option I can think of involves an Android tablet that can be re-imaged back to stock form easily. Samsung units are good about this with the ODIN tool and a USB connection. Just connect the device to the computer, select the appropriate image in the ODIN utility, and it's back to factory-fresh form in a matter of minutes.