As a player who has Overwatch on PS4, I've had a number of friends come over and want to do co-op fights. Sadly, the game doesn't offer that option, which has lead to many asking on a near-weekly basis on Reddit and the Overwatch forums for the mode to be added to the game. Yesterday, Bill Warnecke (Blizzard's Lead Software Engineer) went to the forums and responded to one of the many fans asking this question with a response you may not enjoy reading:
"Local co-op would be really cool but it's not something we're working on right now. Getting great performance on the console for this mode would be a significant amount of effort. Also as Razer points out above, split screen really changes the experience of the game, and we'd have to iterate a lot on that to make it feel great."
So there you have it. While the devs are constantly looking into the game and making additions and improvements, there's really nothing on the horizon for a co-op mode. And they do have a point in saying that the game would take a significant change to the content on the screen once you cut it in half, which may ultimately ruin it for you. Maybe when the day comes that they make a sequel, we'll see it added then.