“A relatively flat, paved bike trail between Tusayan and the South Rim Visitor Center.”
— Lost Justpastnowhere
This is an easy ride through the forest south of the Grand Canyon and might be a good way to work some excess energy out of the kids if you aren't doing any hiking on or below the rim.
We rode from Tusayan to the Grand Canyon on July 26, 2018, and did not encounter a pay station. No fee required when riding a bike on this path.
This is a paved greenway from the town of Tusayan into the Grand Canyon forming part of the network of paved greenway trails throughout the south rim.
You certainly wouldn't come all the way to the Grand Canyon to ride this trail, but it might be quicker than waiting in the long line of cars at the vehicle entrance.
This does make a nice loop with Desert View Drive, and the AZT - Passage 37 - Grand Canyon - South Rim
, which does include a little bit of singletrack.