Use red cent to mean an amount of money so small that it's basically worthless. A waiter might complain that her tips are so bad that she didn't earn a single red cent.
You'll always find this noun in some variation of the phrase "not one red cent." A stingy person announces that he won't give a red cent to any charities, while a crafty person plans to make every Christmas gift by hand, and not spend one red cent on presents this year. The red cent is symbolic, representing an a tiny amount of money. The original U.S. copper penny was reddish and was also called a red cent.