"Andy Dingley" wrote PU squirty foam inside the
tyre. It won't take the weight of a builder's
barrow, but it's OK for garden clippings.

I've used it to re-seat tyres that couldn't get a good enough seat on
the bead to be re-inflated, because the rims were chipped.

Bet getting the exact volume required is tricky :-) I have visions of
exploding tyres similar to those conjured up by the exploding canoe tale.

Henry