I've come across a possible refutation in one of my philosophy books. It goes like this:
The concept of God doesn't have to exist for it to be a concept in our minds. The object of God has to exist, otherwise it is just the concept again, even if we might think otherwise. Therefore, the only way to conceive of God which exists is if God does indeed exist. But this is precisely what the argument is trying to establish - that he exists. Thus, the argument is in fact circular.
The concept of God doesn't have to exist for it to be a concept in our minds. The object of God has to exist, otherwise it is just the concept again, even if we might think otherwise. Therefore, the only way to conceive of God which exists is if God does indeed exist. But this is precisely what the argument is trying to establish - that he exists. Thus, the argument is in fact circular.
"It is the mark of an educated mind to be able to entertain a thought without accepting it" ~ Aristotle