The city's health department has invited suggestions for a special limited-edition design.
Officials said the winning artwork, which will be selected by online voting, would feature on several hundred thousand condom wrappers. The design can not be racy, can not include copyrighted or trademarked images, reports The Telegraph.
Entries are due by Jan 22, 2010.
The city has handed out free condoms since 1971, giving away 40 million of them in 2008.