Plastic.
Thus is the reverse of the usual question.
THAT is how to keep wood from rotting outside.
But you want INDOOR planters.
Get plastic sheet, and without putting staple holes in it, glue it down.
Imagine you are putting a coffee filter in a measuring cup.
Hot glue around the edges.
Make folds where necessary, and glue the flaps down.
Of course, the problem is that it will hold water perfectly.
Too much water and the plants will drown.
Put in sphagnum moss to absorb the excess.