What would be the cure for Addison's disease in someone that can't take steroids?

Why not? Addison disease is due to loss of adrenal function or loss of the glands to disease and replacement steroids are just that, giving the person hormone that adrenal would have made. You did not say why the person can not take steroids. Taking steroid is a as simple as taking a pill.
Odd statement. Steroids are made by the human body as normal stress hormones.At the proper dose level, which might take some tinkering, anyone can take replacement hormones is some form. It would help if you provided more information on why you think the person can't.It is likely a misunderstanding.