There's a product called Florasone that I use with great success wherever I might have gotten results with cortisone cream. I've read a number of reviews swearing that this cream has brought amazing healing almost overnight. It's available in health food sections of many larger stores.
It's got a fairly strong herbal scent, which I don't find objectionable. It's safe to use on kids 2 or older, but at least at first, it's probably best avoid areas where the skin is actually broken – get just up to the edge. Try only one tiny exposed area to find out whether it stings. I can use it right over mild abrasions, but everybody's different. But if you apply it near the eczema, that may be enough to elicit healing in nearby tissues.
I hope you'll keep searching for the cause of the eczema, which could be anything from foods to perfumed or antibacterial hand soap. Many times allergies that show up in skin, lungs or digestive systems also have an emotional component, such as worry or anxiety.