What exactly are 'board books'? do you mean game board type books?
I have a cookbook by Jeff Foxworthy that is printed on cardboard.Kyra Halland said:Board books - books printed on sturdy cardboard for babies and toddlers.
I have no idea where to get those printed. I don't know if print-on-demand exists for those or if you would have to contract with a printer for print runs.
Your books look adorable; I hope you can find something!