Try tropical fruit juices, like Cocona. Pineapple in the Amazon region is quite different to the one found in the rest of Peru, and makes really good juices. Aguaje and ungurahui are also a good choice: you can try everything in the entrance of the Upper Belen central market. You can try also native alcoholic drinks some of them reputedly aphrodisiac. Pasaje Paquito is the best place to buy them.
Para Para, Up and up made with honey.
Aguajina, sweet beverage made with aguaje pulp.