Yes, but you didn't use "coin" with the others, either.
I would say "quarter," "twenty-five cent coin," or "twenty-five cent piece." They're equivalent.
The danger in using "piece" is that it requires context to be understood as referring to a coin, since that word has so many other meanings. If I say "I'd give all the coins in my pocket for a slice of that pizza," the meaning is clear. If I say "I'd give all the pieces in my pocket for a slice of that pizza," the response is likely to be a puzzled "Pieces of what?" The word "coin" is never confusing.