Myers raises what looks, at first glance, like a logical error: he argues that if evidence for God could appear, wouldn't this mean that all current religions that get along without such compelling empirical evidence must be false? But while absence of evidence is not automatically evidence of absence (it depends on how likely an entity or phenomenon is to leave empirically detectable traces), obviously, a God Who intended to make His existence obvious is capable of producing evidence, over and over again, that no one could miss. That we don't see (to cite some examples given by Coyne) routine miraculous healings in response to prayer (to one particular conception of God, and not to other gods or to other conceptions of God), or water being turned into wine by prophets empowered by this God, argues that if there is a God, He doesn't wish to make His existence blatantly obvious. Therefore, a blatant miracle (say, a 900 foot tall apparition of Jesus visible to multitudes of independent witnesses -- which, pace Myers, doesn't seem by itself more out of character for some biblical depictions of God than a pillar of fire or a burning bush), or the sudden commencement of a consistent pattern of less blatant miracles, would be too obvious, too out of the character God has evinced over the last fourteen to twenty-four centuries (depending on which Abrahamic religion one is asking). This would at least argue that the traditional monotheistic religions had been advancing mistaken ideas about God. We'd have evidence of something, but it might not be God as any traditional religion conceived Him.
But perhaps this is, like Doug Adams' "Babel fish" argument for the non-existence of God, taking a philosophical point a bit too far. Of course, both Myers and Coyne note that evidence for God might be interpreted in various ways. Myers, for example, suggests that if he witnessed an unmistakable miracle, he'd be more likely to conclude that he was hallucinating than that he was reliably witnessing a miracle. One might get around this by asking what would happen if Myers' observation was supported by other witnesses as well. When Coyne originally raised this argument, several commentators to his post noted, much more explicitly than he had, that it would be very difficult to distinguish between an actual miracle and the use of unknown technology to simulate a miracle. This is indeed my own response to the problem of evidence for God: as finite beings, any phenomenon that we can perceive and wrap our minds around will be, itself, a finite phenomenon. The most parsimonious explanation for anything -- from accurate, detailed prophecy of the future to healing amputated limbs -- is unlikely to be an infinitely-powerful, all-knowing Being. Laws of nature we don't understand are more parsimonious than an Author of natural law able to amend them or make exceptions to them at will.
And here I seem to find myself siding with Myers against Coyne. Coyne posits a documented series of nature miracles performed by someone who looks like and claims to be Jesus, and asks:
Now you can say that this is just a big magic stunt, but there’s a lot of documentation—all those healed amputees, for instance. Even using Hume’s criterion, isn’t it more parsimonious to say that there’s a God (and a Christian one, given the presence of Jesus!) rather than to assert that it was all an elaborate, hard-to-fathom magic trick or the concatenation of many enigmatic natural forces?It seems to me that the question is, is it more parsimonious to infer a finite but powerful being (possibly using unknown technology) who quite possibly has in the past established himself as the Christian God, or to infer an actual, omnipotent, omniscient, omnibenevolent Being when all you've seen is demonstrations of finite albeit great power? Of course, awed by the impact of the events, and influenced by childhood upbringing, one might not be inclined to be rigorously parsimonious. But I think the underlying principle remains. Establishing the existence of God through the preponderance of evidence is not, I think, logically possible.