And you're right about the dar cuenta part.
AFAIK, dar and rendir cuentas have related but quite different meanings.
As indicated earlier, "rendir cuenta" is to provide some kind of report about the status of something...A common usage: "El presidente rinde cuentas a la nacion" (s/he gives a "state of the country" speech).
Dar cuenta is to provide a justification or explanation for an action taken...as another poster mentioned, the lyrics of a known song say something like "no tienes que darme cuenta" (you don't have to give me explanations or justifications).
In the specific case of "dar cuenta a Dios" this latter meaning is quite appropriate.
A related construction: estar de su cuenta (that is, de cuenta propia) mean that one is only accountable to oneself, that is, one only "da cuenta" (explanations, justifications) to oneself...Los nin~os estan de su cuenta: they are doing whatever they want...have no supervision.