What kind of paint is best for a porch ceiling?

Before repainting it, I'd think you'll need to power wash it to get as much of the old paint off as you can. I think an exterior paint would be what you'd use afterward.

what is the ceiling made of?

If it's just the paint that is cracking and peeling and falling off then you'll need to scrape it down to remove all the peeling paint before you can repaint it. If the boards are rotted then you'll have to replace them before proceeding. Good luck!

Sorry, forgot to note that any good outdoor latex paint will do the job for you.

I agree with Elizabeth, as long as the ceiling is in tact, you shouldn't need to replace it, but you are going to have to remove the peeling paint before re-painting. Have fun!