Abstractly you want an interaction between two parties that will show to the first one that the second one is God, i.e. an interactive proof by God for the verifier who is our rational person.

Answer depends on what you mean by God (prover), what you mean by a rational person (verifier) and what you mean by convincing (what kind of interactions/proofs are allowed?).

Let me explain. 

To show that a book is from God you need to show that the book could not be written by anyone else. This sentence has a universal quantification that can not be checked empirically, so we need to argue that logically. To do this we need to use what we know about God and argue that no one not satisfying those conditions could have written the book, or at least show that this is very unlikely. Most arguments would only show that the prover has certain properties, but this may not mean that the prover is really God, e.g. it does not rule out directly the possibility that it is written by an alien creature with super-human powers.

Same with verifier, our rational person. What kind of actions that person can perform? What are his assumptions about the properties that God has? etc.

The kind of interaction is also important. Sending a book or a written text is one possibility, but there can be more complicated interactions, e.g. other kind of miracles. A text by itself can be a miracle and theoretically a proof that the other party posses very high computational power that is unimaginable that a human can have (here we need to argue what are the capabilities of a human being). It is plausible that the prover is capable of solving a computationally undecidable problem, a problem that we know no computer can solve. But the verifier needs to be able to check the correctness of the proof. A more interesting case is for example a problem that does not have simple algorithms to find an answer but if given an answer the verifier can check its correctness (a.k.a. an NP-complete problem in computer science). If we repeat this process enough times we can be sure that the other party is capable of solving NP-complete problems very quickly, and if you believe in something like Extended Church-Turing thesis, then that should be very convincing.

Interestingly the proof can be very personal and not intersubjective, i.e. God can convince you that a book is from him, but you cannot show this fact to any third party (this is what is called a Zero-Knowledge proof in computer science).

I concentrated on the computational power of God, but one can use other capabilities of God that the verifier believes no one else are capable of, e.g. if God raises month Sinai over my head and I hear a voice that says Torah is from God a few thousands years ago, I would be convinced (though others might not since they believe that what they see and hear is not enough, it might be magic or something).

Interaction can increase the possibility of a proof considerably, i.e. it is much easier to convince if there is a two-way communication, e.g. verifier asks questions or make requests and God answers them. A book can perform as a common knowledge between two parties. For example, if the book is very long and although contains an answer to a question, finding it might be impracticable. But the verifier can ask for a proof of say NP!=P and God would say look at page X of the book. This is probably going to be a much shorter communication than a full proof of P!=NP (you can interpret this as what some people consider signs from God which directs them to answers to their problems or questions). 

I again focused on computational power of a human, but if a verifier has other capabilities they can be used also, they don't need to be computational. 

One last point. Most rationals are somewhat scientifictified, i.e. they only accept arguments that look scientific and are intersubjective. Say a personal interaction with God which is not intersubjective and reproducible might not convince such persons. Aslo arguments which appeal to other capabilities of humans which science does not understand well at the moment, a poem or a picture or a natural even can have a very strong effect on a human, but because science does not certify it they would reject that as a reasonable argument. But it seems that the sender/author of books like Torah or Quran does not share their idea and values psychological and literatural effect more than a scientific argument, maybe it is because science is changes too quickly too much, or probably he has a better understanding of how a human-being's mind works. Probably, these books should be analyzed from that perspective.