Unfortunately, I really don't think it can be done

The reason soap 'stings' the eyes is because of the pH, and, although you can get a very mild bar of soap, you really can't neutralize it, which is what it would take to make it tearless. If you are making liquid soap and getting the pH down close to 7, there is a possiblilty the soap will separate (haven't made liquid soap in quite a while, hope my memory serves me!). Most commercial 'tearless' products are not even soap.
Just my thoughts---would love to hear others---a tearless soap would be great

Susan