Hi Vicky
I bought a machine that looked like that, thinking it would be good to repaint.
By the time I was finished cleaning and oiling it, it didn't need a repaint. Oops!
Try oiling the body with sewing machine oil. (In this case only, I may suggest the regular sewing machine oil, not the triflow everyone likes for the moving parts.) Even leave it on that spot for a few minutes and then wipe away the excess. Try it a few times, I find that the oil seems to build up where it needs to.
After that, if it still doesn't look like you want it to, apply a coat of good quality car wax with a high carnauba wax content in it. I use Mother's products on our vehicles and the sewing machines. I get this from NAPA in Canada, but any automotive shop should have it.
Good luck!!