I am an atheist. I would be interested in seeing what a metaphysical argument for theism would look like. I would also like a counter argument as well, so I can understand both the strengths and weaknesses of both points of view.
For centuries, at least within the Christian tradition, the definitive list of metaphysical arguments for the existence of God has been Thomas Aquinas' "Five Proofs". These are largely arguments for what is sometimes called the "God of the Philosophers," the eternal and unchanging unity of all perfections, and not necessarily for God as commonly personified. Several of the arguments are of the same form; that there cannot be an infinite metaphysical regress (it cannot be "turtles all the way down").
The Argument of the Unmoved Mover - If everything "moves" (changes), there must be something unchanging that is the ultimate cause of all changes in the universe.
The Argument of the First Cause - If everything has a "cause" (foundation) then there must be something that is the ultimate ground of reality. For example, if all matter is composed of molecules and all molecules of atoms, and all atoms of elementary particles, and all elementary particles of quarks, then where do quarks draw their ultimate reality from? What are they grounded in? Are they simulated in a cosmic computer? Are they thoughts in the mind of God?
The Argument from Contingency - Nothing in the world that we see is permanent, all things change and pass away. But if nothing is truly eternal, then how can existence itself be sustained over the long term? Eventually all things must go, and if the past is infinite, then all things should have already disappeared an infinitely long time ago. Therefore there must be a necessary being that cannot pass away.
The Argument from Degree - How can anything be good in a world in which nothing that is perfectly good exists? How could "good" even be judged without a standard? (This is a stronger argument than it seems at first. It's most closely associated with Plato and the neo-Platonists.)
The Teleological Argument - The universe is not random, it bears all the hallmarks of purpose --if this was not true, the rich fabric of our existence would be replaced by dull "static." This argument is influenced by Aristotle, and underlies the modern argument of intelligent design.
There are any number of replies and counter-replies to each of these. The first four are less commonly referred to in modern times because they are essentially idealist, and the modern perspective has made a sharp shift towards materialism. For that reason, the last argument has become the most prominent. The most currently prominent counter-argument is Dawkins' contention that the theory of evolution renders a purposeful designer for life unnecessary. A counter-counter-argument might be that this just pushes the evidence of design back one level (i.e. that the existence of biological evolution is evidence that the universe was designed to be fecund).
My favorite argument for the existence of God is the ontological argument. The short form:
God is the greatest being that could ever be imagined, and we can imagine Him and some things about what he must be like (omnipotent, omipresent, etc.).
Part of being great is really existing. Imagine me telling you about greatest poker player ever, like this guy is nearly psychic, he wins every hand, never flinches, is adored by poker players everywhere. However, if I told you he wasn't real, and instead is just a character in a book that I'm writing, you'd be a bit let down. Clearly he's not really the greatest if he doesn't exist.
If God only exists as an idea in the mind, if he is just a figment of imagination, or a character in a book, then he is not maximally great! He could be greater if he actually existed. Else, he would be like our fictitious super-poker-player - a bit of a let down.
This contradicts the concept of God being maximally great - being the greatest being that could be imagined. Surely a God who really exists, who really parts the seas, really floods the Earth in wrath, really turns water into wine is greater than some story. Thus 3. must be wrong, and God must exist.
It's a really frustrating argument to rebut, hopefully I've laid it out in at least a comprehensible way.
If you want a good explanation of why Classical Christianity is not the claim 'God exists' then I'd recommend God: A Guide for the Perplexed by Keith Ward. It would even be possible argue that this early form of Christianity is not strictly theism or atheism, both being a naive view. As a consequence most modern Christians reject their roots and rarely study them.
For a strict and rigorous logical argument you could check-out the Buddhist sage Nagarjuna. In the second-century he constructed a proof designed to clarify the philosophical foundation of the Buddha's teachings. He logically proves that nothing really exists, (where 'really' is a crucial word) and this would include God. I'd recommend not the original text but The Sun of Wisdom: Teachings on the Noble Nagarjuna's Fundamental Wisdom of the Middle Way by Khenpo Tsultrim Gyamtso. This is brief and clear.
I see no good logical arguments for or against God's existence in modern Christianity. There are some attempts but nothing conclusive. In mysticism the arguments are much stronger and firmly grounded in metaphysics. Of course, mysticism often speaks of God but this is not the God of the Churches of the People of the Book. Even the ancient Rig Veda warns us against this idea. It would be a far more subtle phenomenon, one that would transcend the distinction between existence and non-existence. 'God' would be a choice of words and not a necessary one. For Indian religion 'Brahman' replaces all ideas of an objectified God.
Or you could examine the doctrine of the Upanishads and the arguments found in the commentaries, which do not reify God but promote a much more subtle idea.
I have no wish to offend a lot of people all at once, but have to say that the monotheistic God of most modern scientists and Christians belongs in the nineteenth century or the children's Sunday School. Arguments against this God can be found all over the place in Buddhism, Sufism, Taoism, advaita Vedanta and even in a large body of Christian writings, for instance in Ward's aforementioned book or the Gospel of Thomas.
We see here why so many Christians and Muslims believe that mysticism is the work of the Devil. But for the mystic the Devil would be as much a fantasy as the God of the dogmatic Atheists and Theists.
Here's some words from The Mystical Theology...
. . . [H]e possesses all the positive attributes of the universe (being the Universal Cause), yet, in a more strict sense, He does not possess them, since He transcends them all; wherefore there is no contradiction between the affirmations and negations, inasmuch as he infinitely precedes all conceptions of deprivation, being beyond all positive and negative distinctions. (Dionysus the Areopagite, The Mystical Theology)
And from Keith Ward.
“Dionysius went so far with the negative ways of speaking of God that he even denied God existed: ‘It is the universal cause of existence while itself existing not, for it is beyond all being’ (from his book On the Divine Names). This might seem like nonsense. It would certainly cause a stir if a preacher went up into the pulpit and said, “According to our greatest authorities, God is not like anything of which you can think. In fact, I can tell you that God does not even exist. Let us pray.
But of course the point is to say that God does not exist in the same way that anything we can imagine exists. God is ‘Nothing’, not-a-thing, but that Nothing is not a sheer vacuum. It is that in which all distinctions fade away, but in which they are rooted.” (Keith Ward, God: A Guide for the Perplexed)
Cosmological arguments, for the existence of "God", like those of Aquinas, are functionalism and materialism. They are functionalist, i.e. because they usually focus on the singularity of "God", which is false, due to the weakness of singularity. They are materialist, i.e. because materialist empiricists, usually appreciate Aquinas's 'proofs'. Ontological arguments on the other hand use definitions and are more objective. Here's another ontological argument for the existence of God:
God are "the Creator", therefore God exist because creativity exists.