Hello,
I cannot confirm anything without examination but it can be contact dermatitis or fungal infection of the belly button piercing. Apply calamine lotion or some mild steroid cream the next time it appears and also ask him to take some Benadryl( causes drowsiness) and Claritin. If the symptoms persist then a dermatologist’s evaluation will be the best. Steroids or antifungals may be needed.
I hope it helps. Take care and please do keep me posted in case you have any additional doubts. Kind regards.