The argument from undesigned coincidences

One of the nifty things about the argument from undesigned coincidences is that it's self-contained. All you need is the NT. You don't need extrabiblical corroboration. In that regard it's like a priori theistic proofs. 

Atheists love to put in the mouths of Christians "the Bible is the word of God because it says so", as an illustration of viciously circular reasoning. 

Mind you, I rarely if ever see atheists actually quoting Christians who say that. And if they did, it would likely be some Christian layman. 

However, using X to prove X isn't necessarily viciously circular. Appealing to Biblical authority to prove Biblical authority is viciously circular. 

But to take a comparison, there are probably many undesigned coincidences between The Personal Memoirs of Ulysses S. Grant and the Memoirs of General William Tecumseh Sherman. These are independent of each other, based on each man's firsthand experience.

You don't have to come to either autobiography with prior confidence in the credibility of the author. But if you systematically compare them, I expect they contain many cases where a statement in one memoir sheds light on a statement in the other memoir. That would be highly implausible if these were penned by writers lacking access to the actual events.