If theists are going to have any chance to get a skeptical, critical atheist to suddenly believe in some god, the first step must obviously be to have a coherent, understandable definition of the subject being debated. What is this "god" thing? When people use the word "god," what exactly are they trying to refer to "out there"? Without a coherent, understandable definition it will be impossible to discuss the matter in a substantive and sensible manner. We have to know what we are talking about before we can get anywhere in our conversation.
This, however, is a very difficult task for theists. It's not that they are lacking in labels and characteristics to attribute to their gods, it's just that so many of these characteristics contradict each other. To put it simply, not all of these characteristics can be true because one cancels out the other out or a combination of two (or more) leads to a logically impossible situation. When this happens, the definition is no longer coherent or understandable.
Now, if this were an unusual situation, it might not be such a big problem. Humans are fallible, after all, and so we should expect people to get things wrong some times. A few bad definitions could thus be dismissed as another example of people having trouble getting a difficult concept exactly right. It probably wouldn't be a good reason to dismiss the subject entirely.
The reality, however, is that this is not an unusual situation. Particularly with Christianity, the religion which most atheists in the West have to contend with, contradictory characteristics and incoherent definitions are the rule. They are so common, in fact, that it's a real surprise when anything like a straightforward and coherent definition shows up. Even a "less bad" definition is a welcome change of pace, given how many really bad definitions or explanations there are.
This shouldn't be a surprise when we are dealing with old religions that have developed in the context of multiple cultures. Christianity, for example, draws from both ancient Hebrew religion and ancient Greek philosophy to describe its god. Those two traditions are not really compatible and they are what generate the most contradictions in Christian theology.
Theists certainly recognize that there are problems, as demonstrated by the lengths to which they can go to smooth over the contradictions. If they didn't accept that these contradictions existed or were problematic, they wouldn't bother. To pick just one example of how far apologists will go, it's common to treat some of the "omni" characteristics (omniscience, omnipotence, omnibenevolence) as if they weren't really "omni" at all. Thus omnipotence, which is supposed to be "all-powerful," or the ability to do anything, is weakened to something like "the ability to do anything within its nature."
Even if we set this aside, we are faced with further contradictions: not within a single definition, but between different definitions from different theists. Even adherents of the exact same religious tradition, like Christianity, will define their god in radically different ways. One Christian will define the Christian god as being so all-powerful that free will is nonexistent who we are and what we do is entirely up to God (strict Calvinism) while another Christian will define the Christian god as not all-powerful and who, in fact, is learning and developing alongside us (Process Theology). They can't both be right.
When we move beyond a single religious tradition and expand to related religions, like Christianity, Judaism, and Islam, the differences grow exponentially. Muslims define their god as being so "other" and so unlike humanity that any attribution of human characteristics to this god is blasphemous. Christians, who ostensibly believe in the "same god," define their god with a multitude of anthropomorphic characteristics even to the point where they think their god became incarnate as a human being at one point in time. They can't both be right.
Where does that leave us? Well, it doesn't prove that any of these religions or religious beliefs are definitely false. It also doesn't prove that no gods can or do exist. The existence of some sort of god and the truth of some religion is compatible with all of the things I describe above. As I noted, humans are fallible and it's not impossible that they have repeatedly and consistently failed to describe some god that exists (and is perhaps getting annoyed at the situation). The problem is that the gods with contradictory characteristics aren't the ones that can exist. If some god exists, it's not the one being described there.
Furthermore, among the religions and traditions with contradictory gods, not all of them can be right. At most, only one can be right and only of set of characteristics can be the true characteristics of a true god at most. It is just as likely (and perhaps more so) that none are right and some other god with an entirely different set of characteristics exists. Or it may be that multiple gods with different characteristics exist.
Given all of this, do we have any good, sound, rational reasons to believe in any of these gods which theists keep promoting? No. Although these situations don't logically exclude the possibility of some sort of god, they make it impossible to rationally assent to these truth claims. It's not rational to believe in something with logically contradictory characteristics. It's not rational to believe in something defined one way when the allegedly same thing is defined in a contradictory manner by someone else down the street (why not join them instead?).
The most rational and sensible position is to simply withhold belief and remain an atheist. The existence of a god hasn't been demonstrated to be so important that we should try to believe absent sound empirical reasons. Even if the existence of god is really important, that's not a reason to reduce our standards; if anything, that's a reason to demand higher standards of evidence and logic. If we are being given arguments and evidence we wouldn't accept as justification to buy a house or a used car, we definitely shouldn't accept it as justification for adopting a religion.