Not being particularly religeous, I'm not sure that I see the conflict that you seem to.
In my view, identical twins (the naturally-occurring cloning of one child from its sibling) each have their own unique souls. I don't see why a person's body having been artificially cloned would preclude him from having a soul anymore than being a twin would.
The key here in your comment is "naturally-occurring" - as in (according to my beliefs) "God-intended". Now, we have "artificially-occurring" cloning, with man stepping into the role of God. The question is: Who supplies the soul?