There are serval ways to earn papayas:
1) by logging in daily to receive max. 10 papayas a day
2) complete a survey under "More" option, will get 2500 papayas once in your life time
3) inviting a friend to join the game earns 500 papayas

note: you can also get papayas from "Tapjoy — Super Rewards" or purchase Papaya Pro