For better or worse, many of the arguments are scattered amongst works having to do with atheism as a whole rather than tightly focused on this specific topic. I will caution though, that I suspect philosophical arguments against the existence of God are likely similar to those for his existence — persuasive to those already convinced, and unmoving to those not already persuaded.
All my books are in boxes right now, but two come to mind off the top of my head.
(Michael Martin, ed.)
by Victor Stenger
A few resources you might find useful:
The
at infidels.org
The similarly named
, also edited by Martin.
And Graham Oppy's excellent discussion of the ontological arguments in the aptly titled,
.
While it's seldom stated formally, I suspect the most popular argument against the existence of God is an argument as to the most probable explanation
with respect to other hypotheses. This is an argument which is usually framed using Bayesian probability analysis and compares various hypotheses which might account for the evidence — including fraud, mistake, misunderstanding, and so on, as well as the absence of positive evidence. I think many atheists are vaguely thinking in these terms in rejecting most theist arguments, even if it isn't rigorously stated. (Baeysian probability is not my forte, but there was a paper which I read a while back which walked through the analysis with respect to the fine-tuning/design argument; if I can locate that article, I'll post it.)
Finally, I'm not sure whether it specifically addresses your question or not, but J.H. Sobel's
is regarded as one of the most logically rigorous treatments of the theological arguments. (I haven't read it myself; formal logic and I don't get along.)
And while the following books deal more with criticizing the arguments for God rather than against, you may find them useful.
by Michael Martin is both well-regarded and quite comprehensive. I haven't read it yet, but a brief skim of the reviews at Amazon suggest that it may be a bit cursory in its treatment as well as missing some more current arguments. (I own a copy, and a look at the table of contents seems to bear this out.)
by George H. Smith is another frequently mentioned text. The author's stated purpose being to "demonstrate that the belief in God is irrational to the point of absurdity." I think he does a decent job at that, but his arguments in other areas, including a detour into Objectivist ethics, are less compelling.
If you are studying the philosophy of theism, it's recommended that you familiarize yourself with the work of Stephen Toulmin concerning the nature of argument. While I'm not a big fan of his framework, my impression is that it's very popular among theists, likely because it gets away from a strict form of argument based on logical deduction and into one that is, if less rigorous, kinder to theist arguments. Anyway, Toulmin is somewhat controversial, but an important thinker to know if you are wading into the philosophy of religion and theist arguments, as it is frequently cited. (
, Stephen Toulmin)
And finally, on a related topic, Graham Oppy and Nick Trakakis have written a five volume, 1300 page
which is quite comprehensive as well as being well regarded. The set retails for $415, but used copies can be had for under $150. A substantial investment, but likely worth it if you intend to do serious study of western religious philosophy. (I purchased the set a couple months back, but confess I haven't even opened a single volume.)