The only way that is possible is if the station you are listening to makes available their daily on-air playlist on their own website. There is currently no (known to me) company or product that scans broadcast radio stations and automatically creates a playlist by what is played, or a site where humans contribute heard playlists.
Example - KCRW
http://www.kcrw.com makes available their daily playlists, and archives them, on their website.