One of Swords reports that Overwatch is set to drop on Modern Warfare 3 PS3 on March 29. It'll be available to premium subscribers of the Call of Duty Elite service on PS3.
Then, the multiplayer map Black Box, and two Spec Ops maps, Black Ice and Negotiator, will come to PS3 "on or around April 12." We recently got our hands on those maps, which we wrote about here.
If you're wondering about the vague date, it's because the time for posting the DLC on the PlayStation Network is up to Sony -- it could go live in the morning, or it could go live late at night.