Your sim is mourning the death of another sim.
Have your depressed sim reminisce with another sim. (Same way as you would talk, dance, romance..etc)
Or have a happy sim "listen to reminisce" from your depressed sims.
This works straight away for me however some people have said that it takes a few hours for their sims (I think it must depend on level of relationship with the departed sim... Ie... Less time being depressed if just a friend... Or more time if married)
Let us know how you go with this
Hopefully that has helped.