I would recommend you contact a veterinarian who is familiar with birds. Sorry, but I can only advise you about human nutrition, not animal nutrition. In humans, high blood iron levels can lead to cardiac death in males.
I can though provide you with iron content in foods people eat that animals may also eat. Raisins (2 milligrams iron per 100 grams raisins) have the highest iron content in the list below. However, do you remove the seeds from watermelon? Watermelon seeds contain 7.3 milligrams of iron per 100 grams. I checked other melons (cantaloupe, casaba, honeydew, watermelon and wax gourd) and the iron levels are low. I would suggest that you look elsewhere for the excess iron content unless the birds are eating watermelon seeds.
Cereal grains intended for human consumption are fortified with iron in the US. Sometimes iron fortification is required for all grains prior to being added as an ingredient in a food product. Do the birds get any grains? How about any supplements? Read the food label to see if any grains are fortified with iron?
I would suggest you purchase a good nutrition analysis program with a large database of foods to analyze what the birds eat. Nutrition analysis software allows for custom nutrient goals for humans. If you knew the nutritional needs of different bird varieties, you could add these nutritional requirements as custom nutrient goals. Then, make a recipe of all the foods a bird eats in a day to calculate the iron content. Substitute foods lower in iron content that the birds will eat.