Well that's good. But I'm not sure its enough time. You will arrive at 7AM... by the time customes clears the ship it might be 7:30AM... rent a car... say 45 mins. Getting out of the city and to the rain forest? Might take a hour or two... You would have to have a pretty good plan to do it on your own. Try a private message to "Casanova frankenstein" he lives there and can get you more detailed information and a better sense of how to do this.
If it were me, I'd stick to a ship based tour if available. Some do zip lining and the rain forest and you are guaranteed not to be left behind. It will cost more but the peace of mind of not having to plan it yourself may be worth the extra cost.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013