Medicaid covers medical expenses for qualifying individuals, including medical products and aids. Depending on the special need, diapers may qualify as necessary medical aids. Consult your state's health services office or case adviser for details about your unique situation.
I have a special needs six year old (foster daughter) that is not capable of being potty trained. I receive shipments from Medicaid monthly with diapers and wipes for her. If I needed them I could also get mattress protectors.
Medicaid covers many items for special needs children. The best way to find out if they cover diapers is to call the Medicaid office and ask or you could possibly find out at your neighborhood pharmacy.
Medicaid rarely covers diapers unless someone can't be toilet trained. Other social services, churches, or charities might help. For a permanently and severely disabled child, Disability Social Security might help.
I am relatively certain that Medicaid does not cover the costs of diapers for anyone. However, if you have a severely special needs child, you should be able to receive Social Security on his or her behalf. That should help you cover the diapers.