The so-called draped bust one cent coin from the United States was minted between 1796 and 1807, as the young nation continued to experiment with coin designs that would be appropriate and accepted by its citizens. The large chain cents, wreath cents, and flowing hair (or Liberty cap) cents had not been popular, and Congress established new rules and designs for all coins in 1796.
The draped bust design showed the figure of Liberty in profile, with an ample bosom around which her clothes hung. The draped bust cent coin also showed an eagle on the back. Examples of these copper draped bust pennies can be found for sale from various vendors online, in various conditions; you may also be able to find latter-day reproductions for your collection as well. The draped bust cent gave way to the classic head cent in 1808.