Youth road bike
 

A 26" frame is a huge frame made for someone 6'4" or so. Do you mean a frame designed for 26" tires?

For "road bikes", the wheel sizes are:

24" (520/540 BSD), 650c, and 700c.

The 650c is the road equivalent of 26".

Your 10 year old could probably ride either a 24" or 650c bike. However, with modern frame design, the 650c is probably the best for an older growing kid.

Fuji Ace made some of the cheaper ones.
I believe both Trek and Giant made some.

You can hunt for 650c (and try to ignore similar 650B :eek:)

If you list a location in your profile, you might get some people helping find the bikes.

One other note, looking at 650c, that was also a common track/triathlon size, which has the benefit of lots of high quality components are available. However, there are a number of 650c bikes that are not appropriate for kids.

Look for a small bike with a sloping top tube (generally), or some of the older Treks have small frames with horizontal top tubes.

Here are a few bikes. The Fuji Ace is "cheap". Basic "paddle shifters", etc. If the seller won't ship, there may be people who would facilitate. There is a facilitation thread here somewhere.

https://www.ebay.com/itm/Fuji-Ace-65...s/303084650112

The Cannondale would be sweet, but lacks the sloping top tube, so only for the taller kids, or shorter women.
https://www.ebay.com/itm/Cannodale-C...l/303110420458

This Trek looks pretty nice. Undoubtedly not quite as nice as an expensive adult bike, but not bad for your needs.
https://www.ebay.com/itm/TREK-2200-A...e/303096348511

Oh, and a nice small Jamis.
https://www.ebay.com/itm/2012-Jamis-...e/172804159097

Oh,
And if you are in Eugene, or Portland, I have 24" and a 650c Fuji Ace that could be tuned up and loaned out.

The Fuji is more of a "trainer" bike, but would be fine for most kids, unless they actually start hitting the top of their class, national levels. Perhaps upgrade the shifters?

It's also possible to put drop bars and brifters on a MTB bike and add narrow MTB rims and tires. My wife has a bike like that. Then the gearing is also appropriate. I'm not sure what older group of MTB FDs match up with brifters, but something must because we own one.

One might also look at a third class of racing. Cyclocross, which usually uses drop bar bikes, but with mud. :)

A 24" or 26" conversion would be good for such an event.

One can use road 24" (520 BSD), or perhaps 650c wheels on a 24" MTB.
Or, road 650c wheels on a 26" MTB. Or, of course, simply using narrow 26" tires.

The Fuji Ace is cheap, both in build quality, and actual cost. But, still a solid kid's bike.

It looks like here are a couple of other options:
https://www.bikeexchange.com/s/650c-kids-bikes

Felt F95 (650)
Specialized Allez Jr 650
Norco Valence A 650
Trek Emonda 650

My guess is that it is a tough market for bike shops. Kids grow up FAST!!! And, of course, the used bikes get dumped back onto the used market.

The small women's market may demand some of the nicer bikes, but that is also limited.

Hmmm...

Also add the Trek Madone 4.7 Carbon 650c to that list.

https://www.ebay.com/itm/TREK-MADONE...-/223462089650

Edit: The first photo looks purple. Later photos are clearly blue. Odd way of doing the color balance on that one photo.

That one would make a pretty sweet serious racing bike.

https://i.ebayimg.com/images/g/n6YAA...6K/s-l1600.jpg

Poor kid racing with no bar tape and no pedals ;-)

Seriously, my son went through a 24" and now a 650c bike. Even though they are "expensive", they tend to resell VERY well, especially if they were cared for properly. I think I lost 50$ (Canadian) on the Scott 24" I bought new and later resold.

a local shop has a Specialized Allez that we are going to check out today.

Terry Symmetry has , as I last read, gone to 26" wheels..

Bike Fridays Pocket Rockets are road bikes made around a fast 451 20" wheel

buildable to rider's size.. in Oregon..