Perhaps no one has asked the question because we know there are no good alternatives.  I love the idea of a folding canvas pool, like the dog water dish!  Someone please make this!  

Yesterday (90+ degrees in New England) my two year old ended up sitting in a small plastic dish tub (polyethylene, TYVM) for a while, after we'd come home from the sprinkler park.  Big pools are nice but a little bucket for splashing, sitting, scooping can be good too and certainly uses less water.  A galvanized tub (antique bathing tub?) would be perfect for this method.

Umbra is talking to herself!

Ya, I was gonna suggest the galvanized aluminium tub too... but right now, here in Western Washington, wading pools aren't really needed... seeing as how Mother Nature seems to have confused June for April -.-

the bed of any pickup truck + tarp

Yesterday we filled my 5 year old's wading pool from the rain barrel (nice and clear soft rainwater).  This year my family is using a recycled large closed-top tank as a rain barrel.  We are very careful to keep leaves out of the barrel.  But we made a mistake and put the pool over the grass in our small yard.

To avoid killing the grass from lack of sunlight, today I emptied the pool and moved it onto the patio.  I was able to use a bucket to dip most of the water back out of the pool and put it back in the rain barrel again. After moving the pool (only possible when empty), I could again dispense the water from the rain barrel.  I hope to use the water for a while in the pool before using it in the landscape for watering of plants.  Maybe we'll keep it away from the veggies, with the DEHP content in mind. Yuck!!  Are we running a big bio-experiment here or what.

The pool is a 3-4 foot diameter, 12-14 inch deep type that collapses with just an inflatable "ring", the rest is like the dog dish (single wall with a wire ring around the bottom edge) that Umbra describes. It certainly weighs less than a hard-sided pool, if that equates to anything in this context.

A stock tank would be too deep for most "kiddies" in the target audience.  Kids couldn't climb out of them safely.  What's worse, drowning or dilute DEHP aqueous dermal exposure?

What I hate are all those vinyl inflatable pool toys that seem to attract the yuck algae that grows on them.  I suspect that most of them are discarded after just a few weeks of use.

Umbra, I noticed your answers to yourself tend to be a bit longer winded!  ;-)

While I admit there can be issues with stock tubs being deep, I have to throw out a vote for them as a child who grew up swimming in them. Ours was an old tub put to new purposes, and had a big hole in the bottom that we plugged with beeswax. Worked like a charm. Also, when younger kiddies were present, we just didn't fill the tub up all the way. Only needed about a foot of water in the tub, and a watchful parent to keep young ones from bumping their head on the metal walls. Lots of good memories there!

Running through the sprinkler and squirt gun battle and wetting down the sand in the sandbox to improve building potential were highlights of our backyard hot day experiences, involving no vinyl at all.  

When we were young I lived in West Texas where the heat was brutal.

My sisters and I spent most of the summer in metal wash tubs.

It was funtabulous! My mom still has them!

Umbra,
Some of my favorite childhood memories are from a rual farm in south Georgia - talk about HOT!  My sister and I spent many hours sitting in the bottom half of a whiskey barrel that we filled with fresh cold water we pumped with the old red hand pump.  I can remember the smell of the hot charred inside of the barrel as the first splash of cold water hit the sides.  I think you can find a version of these wooden barrels at local hardware stores - now my folks plant tomatoes and potatoes in those old barrels.