Sometimes straight up and down flannelboards as suggested by Joan above don't hold as well as slanted ones. (I think it might depend on the type of fabric used for the background and the felt pieces. Or maybe it is the humidity?)

You can use Joan's construction instructions to make a flannelboard the is not attached to the wall and put it on a easel so it has a slight slant to it.

Or you can purchase  or make a free-standing flannelboard as shown at right.

Another option is to hang a large sheet of galvanized metal with trim around it (or just use your classroom whiteboard if magnets will stick to it) and put magnets on the backs of your story pieces.