I think system 2 is engaged in coming to believe the bible. In understanding the story, memorizing the parts, contemplating the wisdom of certain passages. Specifically, all the thinking that is deliberate. You can think very deeply and deliberately within some schools of thought that are entirely false. What matters in arriving at the truth is the process - the epistemic standards - during the time system two is engaged.System 2 doesn't seem to be the agent able to make an argument for religion, since religion seems to be strictly System 1. But here I would caution against viewing the two systems hierarchically, kind of dumb vs. smart. System 1 is plenty smart.
The Sunday school children may have an active system two regarding themes/wisdoms/characters in the bible. If they're never taught that the bible should be subjected to scrutiny and that ad baculum is a fallacy, there is no information that could push either of the two systems along the path of critically examining the bible. All you see is what there is. Lack of key information is the problem, not the disinterest of system 2.