All ceiling materials would need to be installed over an intact coat of drywall (with at least tape and 1 mud coat) for fire code code reasons. Drywall IS the cheapest possible ceiling cladding material. 6 mil poly comes in rolls 20' wide to cover everything underneath. A good crew won't need to have their work sanded all that much either.

Of course, if this is merely for aesthetics, then you could do a gridwork of bamboo plywood, covered at the seams by stainless strips. Burlap panels (sprayed with a borax solution) over stretcher bars screwed to the joists. A suspended ceiling gridwork with different colored acrylic panels in it? (Backing it with LED lighing and dimmers for a spectacular effect.) Or even the faux tin ceilings come in some pretty interesting modern patterns.

But none of them could be installed over damaged drywall. But, they could be installed over crappily repaired drywall since you wouldn't have to care if it was pretty when you were done.

What do you want it to look like when you are done? Of course you can nail up plywood with a nice veneer, tongue in groove boards, or wood paneling...but you will have seams. If you are asking if there is something that looks seamless like sheetrock, but doesn't involve an installation mess, there's really no product like that.

Hollysprings you write:

All ceiling materials would need to be installed over an intact coat of drywall (with at least tape and 1 mud coat) for fire code code reasons.

Not all jurisdictions require ceilings over drywall. Most firecodes call for a material with a specific fire rating. That is to mean that it takes "x" amount of time before flames can penetrate the wall or ceiling. Metal or fire rated ceiling tiles for example doesn't need fire rated drywall beneath. So that leaves many materials available for construction. The posters question is cloudy to say the least, as in how long is a rope?

LOL!