You can use sunflower oil instead of butter, or some of the margarines are dairy-free, can't remember which one but I used to buy it for DD. I remember buying it in Tesco. Be careful if you do buy the margarine because some do have milk products in them.
Weigh the eggs in their shells, then weigh out the same amount of marge, caster sugar and SR flour + a teaspoon of baking powder if you like, mix all together, put into cake tins (use those greaseproof tin liners), bake at 180C for 20 minutes or until they spring back, stick together with butter cream, jam or whatever he likes and cover in roll-out icing.
Or do it the proper way:
www.bbc.co.uk/food/recipes/spongecake_1284
Double up on quantities if you want a larger cake and substitute the dairy-free marge for butter.
I think M&S do a dairy free one but they are quite expensive.
Good luck.
glad you found something.