Here are all the songs given airplay time by KCRW DJs. The database updates every few minutes so if you're looking for the most recent play, sit tight.
This search filter will help you find a song played on the radio when all you remember is when you heard it.
Plug in the date you heard the song, the approximate time, and give a number of hours (whole number!) of an uncertainty window (i.e. 1 hr will give a 2 hr window around the time you chose).