Birds in the wild compete for every morsel of food they eat. The fruits in in the jungles are not cultivated to be pleasing to the human palate. They are wild fruits that typically contain less sugar and are usually eaten unripe since ripened fruit is a precious commodity.
Since we only have access to cultivated fruit we should try to select varieties that are not packed with sugar so you may want to look for heirloom varieties or fruits types intended for cooking.
Tropical fruits are usually good choices even though they likely have high sugar content but they're good because they are often nutritionally superior. Canteloup, Mango, Cherries, and Passion Fruit are all good choices that are usually available.
The fruit list is long and can vary from region-to-region. Whatever you think of trying, look up the nutritional value and use that to decide. Birds are opportunistic eaters, their diets change with the season so don't worry about not being able to get that pomegranate that's not in season. Select something that IS in season and make sure it is nutritionally a good choice.
More About Fruit ...
A Word on Digestion ...
Yes,your psittacine CAN effectively digest carbohydrates and sugars. They are an important energy source and necessary for a balanced diet. Like everything BALANCE is key so look for good nutrition and pick fruits with lower levels of sugar.