Paint/stain used for wooden planter?
I'm not saying this is the best, perfect solution, but if you do want a paint to protect the inside of the planters and not harm the plants, you can use a spray on "pruning seal" product.  It's designed to seal up large wounds in a tree, but the spray can will also mention spraying the inside of a planter to waterproof it.  I've used it before to waterproof the inside of a wooden bowl to create a small cactus garden.

You can apply several light coats to build up thickness.  If you try to spray it too thick, it takes forever for it to dry.

(randomly picked example image, comes from several brand names and is the same stuff as far as I can tell)