Not super close to Cochin but on the west coast you can dive in Goa and Karnataka (Netrani Island). The latter is a lot better in terms of visibility and stuff to see but is a little less convenient to get to than the local Goa diving. A lot of dive outfits in Goa also organize overnight trips to Netrani Island. If you're already somewhere in Goa and have a day to spare, it's worth checking out the local diving. To go to Netrani, I think having 2-3 days is better.
I've only dived in Goa a couple of times (boat dives from Bogmalo Beach, close to the airport) and it's OK diving. November to February is the best time to go - my wife and I went in April once (end of the season) and the conditions were pretty bad. I'm going to be in Goa next weekend and will dive the same location - will report how that goes.
Best,
elgoog