Scroll boxes are sually made of Paulownia tree. They are called kiribako (桐箱). The wood is very light and delicate, similar to balsa.
They come with paper wrapping made of thick paper.
Making a box for a scroll is quite a challlenge, as the carpenters do not use glue for all the parts, only the outter frame. Parts fit perfectly into their places. Expensive boxes are not glued at all, only assembled by means of small wooden bolts.
I forgot to add that you may also want to look for fuuchin (風鎮) which is a "wind wieght" being hanged at the sides of the axis, to stop the scroll from dancing on the draft. Some of those can be quite pricey.
