An improvised coin cabinet can be made very cheaply from an office shallow drawer filing cabinet - the type intended for papers in an office - lined with baize or felt.
Rotho produce a ten-drawer unit, each drawer being about 20 mm deep, the whole cabinet being roughly 145 x 290 x 300 mm in dimension, large enough for a sizeable collection of coins. Each drawer is fitted with a label which can be used to identify the contents of individual drawers.
Lining the drawers with baize or felt stops the coins from skidding about and getting scratched by the plastic surface.
To line a drawer, cut a piece of material slightly smaller than you need, but leaving enough for a slight overlap up the inside wall of the drawer. This can then be glued to the plastic drawer using a small amount of PVA glue (be careful not to apply too much or the glue will soak through the material), and the material stretched gently to keep it taught and crease free. It is as simple as that.
An even cheaper alternative, which requires more effort to make, is to use old empty matchboxes, glued together into a larger cuboid arrangement, and then the whole top and sides of the arrangement painted or covered with decorative paper or plastic to make it look nice. A knob for the front of each small drawer can be made by inserting a split pin through the front of the matchbox drawer, so as to allow the draws to be easily opened. These drawers can then conveniently hold a single coin each. Gluing the whole structure to a heavy wooden base will provide some added stability to what can otherwise prove a rather light weight cabinet.