If your atheism is based on reason and evidence, then what sort of evidence or arguments would it take to get you to change your mind? What would it take for you to stop being an atheist and start believing in God?
Atheists are frequently asked what it would take for them to finally believe in the existence of some god. That's a difficult question to answer because "god" can mean so many different things. An atheist's first response should thus be to ask what the theist means by "god." That doesn't end the problem, though, because if we are talking about the traditional omnipotent, omniscient god, there doesn't seem to be any evidence that could rationally justify belief.
The first thing that needs to be understood is that any effort to rationally justify theism must focus on some god in particular, not "god" in general. You can't "prove" theism because "theism" is a mostly-empty concept. Theism is the belief in at least one sort of god. There is no proof of theism that isn't a proof of some specific god or gods. In order to prove theism, you have to have in mind some set of characteristics of some type of god.
It's ironic that whenever those characteristics are taken into account, apologists often begin a quick retreat in to a vague theism which may be immune to critiques, but is intellectually uninteresting. Theists asking atheists what it would take to believe cannot do this; instead, they must specify what sort of god they have in mind and then ask what it would take for an atheist to believe in that god in particular.
A further, though minor, complicating factor is how the nature of the proof is entirely dependent upon the nature of the claim. If someone claims to have certain evidence of the existence of their god, then they have set the bar pretty high for themselves. If someone merely claims that belief in their god is reasonable — but not necessarily mandated — by the available evidence, then they may not have a tough job to do. So a theist asking what it would take for an atheist to believe should also specify what sort of belief they have in mind: the belief that some particular god definitely exists, or merely that some sort of god probably exists.
Unfortunately for most theists, the sort of god they have in mind is one which no set of evidence could reasonably justify believing that it even probably exists, much less definitely exists. The problem lies with the extreme nature of the characteristics attributed to their god: omnipotent, omniscient, omnibenevolent, etc. What sorts of events could possibly point to the existence of an omnipotent or omniscient god? There are obviously events which theists typically focus on, like the creation of the universe or particular miracles found in the Bible, but none of these clearly require an omnipotent or omniscient god.
Even the creation of all existence would at most only require accepting the existence of a very, very powerful being — and even then, only at the time of creation. Nothing about such an event necessitates belief in an omnipotent, omniscient, omnibenevolent, or even currently existing being. The same is also obviously true if we consider far lesser events like turning water into wine, rising from the dead, or even arranging the stars into a message directed specifically at us.
Indeed, it isn't even necessary to have the power to accomplish such actions — all that's necessary is the power to manipulate our brains into thinking that the events occurred. The power required for that isn't anywhere remotely close to the infinite, all-encompassing power typically attributed to the gods which believers say exist. The problem isn't that believers are setting their sights too low with respect to the miracles they are looking at, but rather that there simply isn't any event that would necessarily require something like omniscience or omnipotence to explain it.
Theists have defined their gods in a manner that is simply too extreme to justify on any evidential basis — a manner that virtually ensures that no set off evidence could ever be counted in favor of its existence. Even worse, it's not clear that they even realize this.
Theists who ask what kinds of proof are required to defend their position seem to me to be missing the point: if they have to ask, that suggests that they haven't given the matter much thought already. This is true even if we set aside the fact that there is no evidence that could be presented in favor of their beliefs. If we accept, for the sake of argument, that such evidence does exist then there is still something wrong if theists themselves haven't thought about the matter enough to have already come up with the appropriate evidence.
Who accepts the truth of a proposition without already having a good idea what kinds of support are required for such acceptance? When scientists propose the existence of something — a new particle or force — they also try to provide tests that would provide evidence for or against their theory. They have an idea of what sorts of facts would either count in favor of their ideas or count against them. This isn't a specialization unique to science, but should instead be treated as a minimum expectation from anyone claiming that something exists or is true. Even if they don't have the evidence in hand, they should have some idea of what the evidence would be or look like. Otherwise, we cannot reasonably credit them with having a rational, justified belief.
Finally, we should consider the fact that this question is sometimes asked with an eye towards showing that atheists have no idea what might get them to change their minds and, therefore, don't really have a rational, reasoned position after all. This same critique can be turned back around towards religious theists, though. How many of them have an idea of what it would take to get them to stop believing in their god? If they have no idea what would falsify their belief, then is their position genuinely rational or well-reasoned?