I have two. A vintage Dawes and a Vintage Raleigh Record. The Dawes is up and running, but the Raleigh needs one spoke and new bearings/grease all around.
These 24" Junior Road Bikes (use as ebay search terms) are pretty rare, and so are their wheels. They are 540 tires, AKA 24x 1-3/8". Tires and tubes are available, but alloy rims, not so much. Steel is probably better for kids that age as they get used to twitchier road steering.
I was recently discussing whether 559 26" MTB wheels would fit with skinny tires, but the front fork is set for 90mm juvenile axles, not regular 100mm ones, and I'm not so into playing with the fork as I am with spacing a rear triangle.
Was thinking about selling the Raleigh. It's worth fixing up.
Snapshots:
The Dawes:
The Raleigh: