Piston rings are normally made of cast iron, Meehanite being one type of cast iron. It doesn't matter whether it be gas engines or steam or diesel, they are usually made of cast iron. The high percentage of graphite in the iron helps with lubrication, especially when used with cast iron cylinders. Plastic rings probably would disintegrate in short order, the temperatures are elevated by the steam in the first place, plus the added heat of friction would cause the plastic rings to melt at the ring face where it meets the cylinder wall. Plastic rings might work for a short time if the engine is run only using compressed air, but steam would probably not work very well at all.
Graphited string packing, as mentioned earlier, works well in small steam engines, but once you start getting into cylinder bores of about one inch or more, the string packing just does not work too well.
Some individuals have had good luck using neoprene O-rings for compressed air engines, but Viton O-rings seem to work much better, especially if running on steam. When using O-rings it is important to remember that the o-ring does not need to be 'squeezed' into the bore, it should not fit overly tight.
Regardless of what material you are using for rings, it is important to remember that you do not need the high ring pressures with steam or compressed air that we are used to seeing with internal combustion engines. The rings merely need to seat and close the gap all the way around the piston, but do not need to exert the sealing pressure that is typically used with gasoline engines. I read a very interesting article on this somewhere, though I do not remember where. If I can find it I will post a link to it if it is available online.