1 Dark Leafy Greens Some of the best sources of potassium are dark leafy greens such as spinach, which when cooked has more than 800 mg of potassium per cup; bok choy, which contains around 600 mg per cup when boiled, and Swiss chard, which has almost 1,000 mg per cooked cup.side from energy and potassium, bananas are also a good source of fiber and vitamins B6 and C. For other high-potassium fresh fruits, enjoy cantaloupe, kiwi, oranges, and strawberries. 1  Getty Images Avocado If avocado isn’t a staple in your house yet, you should probably start adding it to your grocery list.