I haven't personally tried this but I was interested in it because there has been some success with psoriasis which I suffer from. I dont have eczema but it was what the "posters child" (on another tip forum I am on) suffered from and many others tried it most I think with some success.

A tablespoon of molasses once a day. It has to be pure molasses which you can get from many health food shops or even some coles and woolies sell it. Be careful though as there is an sweet or and unsweet type. It doesnt matter which one but the unsweetened is very hard to get down.
The "poster" stirred it through a glass of chocolate milk for her daughter and said within a week it was gone and this was from been covered. A aboriginal elder had told her the tip and she was very skeptical but thought what have I got to loose I have tried everything?!

Many others also gave it a go and many of them couldnt thank her enough for such an easy solution to something they had been fighting with for years.

As I said I havent tried it but I have been on this other site for years and have discovered many useful and handy tips and ideas so I thought I would let you know.