You asked this in completely the wrong way. The whole point of this riddle is that when you say "One of them is not a quarter" the listener takes this to mean that neither of them is a quarter. However by following this with "What is the other coin" you immediately undo this line of thought and the listener realises that when you said "One of them is not a quarter" you were talking about exactly one of the coins, making the solution completely trivial.
You should say "One of them is not a quarter - what are the coins?" (put the emphasis on "not" ) and then when the listener gives in you say "A quarter and a 5c, I said one of them wasn't a quarter, but the other one is - hah! fooled you" (this time the emphasis is on the first "one" ).