What are the possible causes of dark circles under a child's eyes, and how do factors like sleep, allergies, and genetics contribute to this condition?

It has to do with an iron deficiency. It does not mean that the child has anemia, but they may have anemia. Iron is involved in different chemical pathways and enzymes.  

Iron deficiency symptoms 

• Fatigue 

• Dizziness

• Pale 

• Irritable 

• Ice cravings

• Delayed growth 

Children should not take iron supplements from a drug store for dark circles under the eyes. Always do food-based iron, a food-based complex, or just the food. The child should also be consuming vegetables because when someone has an iron deficiency, they probably have other deficiencies.