Natal Plum, Feijoa (pineapple Guava), Dragon Fruit Cactus, Pomegranate, Edible Canna, Taro, Chaya, small Citrus trees, Prickly Pear Cactus, Chili Pequin (Bird Pepper), Fig (pruned small)
If I were growing in the tropics, I would try a lot of things from this website:
http://www.tradewindsfruit.com/tropical-fruit/ I'm currently growing Edible Canna from seed I bought from them. Unfortunately Canna like a lot of water, so I'm growing mine in a tub, not in the ground. Same with Taro, but that has to be grown from a tuber. I bought mine at a market in the city.
Dry conditions really limit what we can grow. If I remember right, you said you don't want to irrigate. Natal Plum, Feijoa, Prickly Pear, Pomegranate, Bird Pepper, Fig, and Citrus can grow with very little water once well-established, but might not produce much fruit, because fruit is mostly water. My Prickly Pear don't even like to grow new pads (which are edible) unless they get some water or decent rains.