If the leather is really looking bad, then I would suggest taking a wood chisel and removing it, then sand down the wood using a palm sander to make the surface smooth and then prime and paint using no less than two coats of the top coat for paint. Since this is to be used in a child's room, then I would recommend using paint that is at least a semi-gloss sheen to it so that it can be washed. Using a latex primer as well as paint should be fine.
I like to use Sherwin-Williams paint products because they are of such high quality. If cost might be an issue, then Sherwin-Williams also makes Dutch Boy paint products, which are also very fine quality. Dutch Boy paints are available at such places as Menards or Lowe's.