Parasol frames were commonly made of wood or whalebone. Overall, the covers were rather simple, without ruffles, lace, or fringe, as seen in the 19th century.
Believe me when I say that there is a small amount of information available about parasols, and I don't know of any books on them. When seeking a parasol to complete your polonaise, your best bet is to buy vintage, but be warned-- many times, parasols can be pricey. The black and white striped parasol I bought yesterday cost me $40 after I'd haggled it down, and the condition is not perfect- the cover is faded to an almost greyish brown stripe and there are a few small holes. However, the frame and spokes (aluminum and wood) are in very good condition, which seems to be the main thing when buying. On the other hand, I bought a vintage 50's blue silk Asian style parasol for $7 and feel like I got a decent deal. So it all depends on where you look and what you find.Essentially, as with any accessory you buy/make to complete your historical outfits, do your research! Some more resources on 18th c. parasols can be found here, here, and here! If anyone has anything to add, please let me know in the comments!