If you are familiar with this blog, you will know I think we can prove beyond reasonable doubt that there is no God just by appeal to empirical evidence (and I also think it is possible to prove there is no God by conceptual means). See The God of Eth.
Incidentally, I think maybe Dacey at the beginning misses out a third kind of proof that X does not exist. He mentions:
(i) conceptual proofs
(ii) proofs based on looking for a thing and failing to find it (note this seems to require X be observable, which God supposedly isn't)
But there is also this method:
(iii) show that if there were an X, there would not be Y (Y being observable). Y is observed to exist. Therefore X does not exist.
Note that (ii) takes absence of evidence to be (under certain circumstances) evidence of absence, whereas (iii) does not. My God of Eth "proof" is of the third kind.
P.S. Perhaps (ii) should also include: if there is an X, there would be Y (observable). Y is not observed. Therefore X does not exist. This does not require God be observable (as Dacey's formulation seems to require). But it is not as effective as (iii), as one might insist that our failure to observe Y does not show Y does not exist (again, we are still treating absence of evidence as evidence of absence). However, if Y were something that would be observable everywhere if God existed, such as "an absence of gratuitous evil", then the observation that there is no absence of gratuitous evil round here would directly entail there's no God. (iii) thus becomes a variant of (ii) after all.