With most frameless packs, you can use just about any pad. Foam or air. Normally you just fold them in thirds. Or you can by a small "sit pad" do use as the back/frame. But a sit pad is a single use item.
Some people just roll their pad as a cylinder and place it in the pack, and put their gear in the center.
You are not going that far, your son may have a book bag pack that would work just fine. That is what I used when my kids were small. Or just look for a very basic rucksack.