On Lake Gatun, you have 3 options -- one is to arrange a tour with the Smithsonian to go to Barro Colorado Island which is run as a research lab. Its probably your best bet to see wildlife. You do have to reserve slots as far in advance as possible. Its around a 6 hr affair with lunch included.

Another option is the one run by the Gamboa Resort, which take you on little boats around the lake. More touristy than the other one, but is easier to book.

The third and more adventurous option is to arrange it on the spot in a town called "La Arenosa". You drive about 1hr on the highway out of Panama City, past La Chorrera town. It's a small fishing port on the other side of the lake from the two previously mentioned ones. You can easily hire a small boat or canoe. They cater more toward fishing groups but can take you to more unexplored areas of the lake.

As for Coiba, I dont think they let you stay on the island, even camping. Best bet is to arrange a trip from Santa Catalina.