https://en.m.wikipedia.org/wiki/Aircraft_fabric_covering This article states several early aircrafts that successfully used cotton as wing skin including Wright flyer. "Colditz Cock" glider had its wingskin made from bedsheets plus this guysused bedsheets to make their wingskin and the plane kinda took for like 2 seconds. Can a good,strong bedsheet successfully replace tedlar in an airplane without any problem?
The earliest covering systems were actually bedsheets... well not literally bedsheets, but the fabric was linen. The Wrights used muslin, a tightly woven cotton used for womens' unmentionables. Grade A cotton came later after linen, then polyester after WW2.
I'd say the cheapest alternative to Tedlar might be to use commercial grade polyester fabric of a suitable weight that can be heat shrunk and use premium exterior latex house paint as the filler system. You'd have to use polyester instead of cotton or linen because on those fabrics it's the dope coating that shrinks the fabric to make it taught and I don't think latex paint will have the same shrinking effect.
Instead of aluminum powder added to the dope for UV protection as is done for normal airplanes, for latex you add carbon black to the base coats.
Anyway, I'm not making this up. Latex paint has been used on homebuilt aircraft with success http://www.flysquirrel.net/piets/paint/paint.html. I've seen that Peitenpol in the article at Oshkosh and it looked pretty good. The article notes that the latex finishing system was actually lighter than an actual aircraft finishing system like Polyfibre.
Absolutely you can use a fabric for covering and airframe. I used to build large scale R/C aircraft much like they used to build real world aircraft. I used fine silk to cover the wings, elevator, tail, and fuselage. I used epoxy to adhere it to the wooden airframe and then later apply some kind of lacquer, which serves to shrink and pull tight the silk and also makes it airtight. This can then be painted or not. Silk is a very strong lightweight material. The performance is actually probably better than many modern materials, but probably would not hold up to the elements as well over time.
Fabric coverings need to be strong enough to handle the load to which they are subjected. As an example:
Piper PA–18s, for example, emerged from the factory wearing Grade A cotton fabric tested to withstand a minimum of 80 pounds per square inch.
This super cub cruised at 130mph with a wing loading of about 10lb/sqft.
Fabric wings, particularly cotton, are often also "doped", meaning they are painted with a material that shrinks, preserves and makes the fabric less permeable to air.
Classic and antique aircraft got coats of plasticized lacquer called dope, a flammable material that served to tighten the fabric and provide some protection from the elements; paint was applied over the dope.
Some ultralights with UV resistant nylon coverings do not take this extra step. If your aircraft is only to be used a couple of times, preservation is less important.