Someone above you suggested velcro. Which I have used to stick things to a smooth wall or wooden closet door -- with good results, until the heat of summer breaks down the adhesives.
Command strips would seem ideal for the application. Except that my 8 x 8 foot board has the felt fabric wrap around to the back side, attached with vast quantities of hot glue, and that whole mess is best held up with screws and not elegant little 3M products.