I always assumed Penguin died from the fall,and the stuff he was coughing up was blood. gotta remember,this was the heyday of the MPAA, who were against all types of blood and gore (but not sex or nudity).
Green blood lol? Even though you can see red blood on his face and head in the very same scene;
http://oi62.tinypic.com/23jh8qp.jpg
Returns was not shy about showing blood, like when Penguin took a bite out of that image consultant's nose, or when Catwoman clawed the face of the mugger.
In the two disc special DVD release, the behind the scenes footage shows Danny DeVito and his make-up artist Ve Neill in the make-up trailer. In the footage, they discuss how the black stuff that he spits throughout the movie is bile that's a result of a condition that the Penguin has. So it's not a huge leap to say that the impact of the fall (he fell on his back, if I remember correctly)
He fell sideways into the water, not on his back:
would have made him spew up a ton of bile if he's already drooling it from the first time we see him.
He is not drooling it the first time we see him:
Nor is he drooling any black saliva at all for the majority of his scenes:
The fact that he's just emerged from a tank of water would add to the volume and spread of the bile as we see in his final moments.
He's spewing up green gunk, not the black bile he usually dribbles a bit on his chin in a small handful of scenes. So why would being submerged in water cause him to be consistently drooling up a river of green liquid? If it was his bile and was naturally green then his teeth and lips would have had a green tinge all throughout the movie, not a black one.
Not to mention listen to him during the whole scene. He sounds like he's slowly choking. It's also implied that the heat is getting to him since the fan that was cooling his lair was destroyed. "The heat's getting to me....UGH!"