How do I repair black painted furniture that is peeling off?

Chances are steps were skipped on the prior paint process. I never get rid of anything that can be fixed unless giving to another diy person.

Strip the paint, Citristrip is one of my go tos. Lightly sand. Wipe down to remove any dust. Prime (do not skip this step), then paint. Depending on the item, I would use a semi gloss or gloss paint, easier to wipe down when needed.

Sand down to good surface & repaint with a good colour paint of choice!

I would make a good assessment of the wood underneath, and be sure that it is worth the work you are contemplating. Stripping and sanding is in my opinion a ton of work! On a chair for example, there are so many rungs and hard to reach places it really requires getting in there by hand..... each spot several times....(strip, sand, paint)

I have a very old rocker than does have many layers of paint and you know that because the previous paint jobs did not remove all of the old layers. Not that it matters so much, but you need realistic expectations.

Even if you are talking about a simple table with a lot of flat surface area, I would still be wary of the work needed for the legs.

If the underlying material is particle board i would get rid of it and go estate sale shopping!

PRWins Hi,. Strip the furniture of the paint, and sand it. Paint as much of the furniture laying down. You probably need a primer, check with Home Depot or Lowe's paint department. Aloha!