High denomination coins, made of precious metals, are highly feasible. I can easily see $5, $10, $20 in silver and $100, $500, $1,000 in gold.
Paper for low denominations, not so much so. A paper note costs about 2 cents to produce and doesn't last very long. The lower the denomination, the shorter the lifetime, because it changes hands more often.
That said, some countries have had paper-only systems, and China still has paper notes in denominations as low as 1 fen (1/100 of a yuan or about 0.15 cents US), though aluminum coins co-exist with notes for low denominations. For some reason, according to a travel guide I read (sorry, I don't remember which one), paper is more popular in some regions of China, and coins mostly circulate in cities with rail transit systems, presumably to operate ticket machines/turnstiles.