Earth and water could be golemcrafting. Earth to provide the material and water to provide the impetus to move. Earth and Air could be Transmutation, as together they can change the substance of the item. Or if you thought it could work, move necromancy to air and earth (air representing breath of life) and earth and fire could be transmutation.

I'm trying to figure out which system you are using to delineate schools of magic, because I can't figure it out, so I don't know that my suggestions will be very helpful. Also, have you decided how divine magic is going to work with this setting?