Acrylic is what almost everyone uses on air dry clay and it is what most manufacturers name on their own packaging. The parts that go wrong are timing and expectation: painting a piece that is still damp, and expecting a varnish to do what a fired glaze does. Both are easy to avoid once stated plainly.
Wait until it is dry all the way through
Paint on damp clay traps water underneath a film that will not let it out, and the result is peeling, bubbling or a piece that never fully hardens. Test it the way you test for drying generally: the clay stops feeling cool against the back of your hand and the colour is even with no darker patches. On anything thick, wait a day past that point. This single delay prevents most painting failures.
Which paint, and why acrylic wins
Acrylic covers well on a porous surface, dries quickly, does not need a solvent and comes in small quantities, which suits an object that needs very little paint. Poster paint chalks off, and oil paint takes days on an absorbent body. Gesso or a coat of watered-down white acrylic first will even out absorbency on a body that drinks the first coat unevenly, which most bodies do.
Sealing: water resistant, not waterproof
A varnish, an acrylic sealer or a resin will keep splashes and damp air out, which is enough for an ornament, a trinket dish or a pot that holds a plant in its own liner. None of them makes the object hold water, because the clay under the film is still soluble and any chip or scratch lets water in. Anything that will be washed, filled or left outdoors wants a fired body instead.
Sanding before painting, and the dust rule
Most people smooth a dry piece before painting it, and this is the one step in the whole process that carries a genuine health point. Dry sanding air dry clay releases respirable crystalline silica. Sand with a damp sponge or fine wet paper instead, wipe the surface rather than blowing it clean, and the finish is better as well as safer, because wet sanding does not leave the fine scratch pattern that shows through paint.
Questions people ask about air dry clay
What paint to use on air dry clay?
Acrylic, on a piece that is dry all the way through. A thinned white first coat evens out absorbency on bodies that drink unevenly.
How to paint air dry clay so it does not peel?
Make sure it is fully dry before you start, and put the first coat on thinly rather than heavily. Peeling is nearly always trapped moisture.
Does sealing make it waterproof?
It makes it water resistant. The clay under the seal remains soluble, so anything that will be washed or filled needs a fired and glazed body instead.