Natural ways to keep the ceiling cool during summer
I assume you mean the roof is exposed to the sun...and that in turn is heating your ceiling?

If so, options:


make sure the roof is reflective (white/metallic) rather than a dark color (which absorbs heat)
make sure the roof is insulated
If the roof can support a green/planted roof, consider that.
plant trees to shade the roof (obviously may take a few decades to fully work)
create a cold roof (some form of secondary roof to shade the one below...in many climates this would be an attic type constructions...but almost anything could work...a covered roof deck, for instance--or even just a vented second layer such as standing seam metal panels on top of spacers to allow for airflow underneath.)


Once the ceiling is warm, it means the heat had already entered the living space. Can't really cool the ceiling at that point without getting the heat out of the living space. Exhaust fans could help...along with perhaps a ceiling fan. Cross ventilation with windows/vents. Etc.