Assuming sci fi apoc?
Smartfabric- used for clothes and insulation-
Holds the shape and size of whatever it’s programmed for-
Perfect for all sorts of useage-
But if the code is corrupted or a single glitch is encountered- that puffy padding won’t ever be coming off~!

It's actually more of a regular apocalypse, so I was hoping for ideas for how you could make a diaper out of normal household fabrics and plastics, but a smart-fabric diaper is an idea I could use in the future, too.

If we're doing Fallout logic, rubber and cloth would probably work. Leather could be good as a 'waterproof' backing if treated right, with fabric inner. As for recreating disposables? Eeeeeh...

You can find tarps all over the place, if you consider a setting around the US, and those are waterproof so it could make a nice external backing. Part of the problem though is making something that won't leak easily, and for that you'd probably need some kind of latex band of some kind to put around the leg holes. As far as the stuffing goes, I would assume that there would be towels in the abandoned houses. Towels aren't exactly the first things you take with you when the nuke sirens start going off. That is, unless it's in the hugely distant future, in which case not sure if you'd find towels. I suppose, you could use sponges - they are natural and grow in aquatic areas, and the synthetic ones we have now are pretty durable and probably wouldn't waste/rot away easily. Though it would probably make the end product thicker than the kinds we have these days. To keep them up, I'm sure you could find some kinds of pin-like objects around the place somewhere. Or old buttons could be sewn on, if you can find some thread, or would be able to unravel something with sturdy thread on it.

Just some thoughts. Interesting situation to think about.

This basically nails it.

Addendum: You could probably cut open a bungee cable to get elastic strings. They're pretty durable and would probably last - only problem is maaaybe the elastic will have dry-rotted, but again depends on the length of time.

This is my idea for the materials of a diaper, it's mostly items/junk used in Fallout 4, but hey, Fallout is an post-apocalyptic game.
So the junk items are;
Cloth
Plastic (Since diapers crinkle due to the plastic nature)
Ballistic fiber which makes the diaper very durable, and hold any weight
and finally Adhesive/Duct Tape, since they both keeps the diaper together so it wouldn't fall apart.

I hope this helps.

well if its the apocalypse then looting houses is ok so...
pull-ups? just use the materials inside to make one that fits