The book itself would have to have the following properties:

1. The book has always existed in every human culture.
2. Everyone can read it, whether they know how to read or not.
3. The book is clear and unambiguous on every point, and everyone who reads it agrees that this is so.
4. The book is not published by any known human agent, but it exists anyway, and no human is ever unable to obtain a copy. That is, the book itself is not subject to the laws of physics.
5. No other book meets this criteria.

While this wouldn't prove that the book was written by an omniscient, omnipotent being that created the universe, it would definitely prove that the book is not written by man. So it's written by a being that is at least godlike.

An edit, based on muz's comment. It occurs to me that the questioner mentions "a god" as opposed to "God". In that case I suppose we could have many such books, and the best way for a rational person to be convinced that it was written by a god would be for the god to claim credit. For example, if there actually were an Athena and her powers and attributes were sufficient to demonstrate her godlike nature, then if she appeared on the Daily Show to promote her book, there wouldn't be a rational reason to doubt that she wrote it.

My first answer is based on the assumption that the book itself has to be proof of the existence of the god in question.

The book itself would have to have the following properties:

0. The book manifests as a tangible object--paper, clay tablets, etc.
1. The book has always existed in every human culture.
2. Everyone can read it, whether they know how to read or not.
3. The book is clear and unambiguous on every point, and everyone who reads it agrees that this is so. This means that there are no incidents, in history or experience, where two humans have ever disagreed about what the book says or how to apply what it says to a given situation.
4. The book is not published by any known human agent, but it exists anyway, and no human is ever unable to obtain a copy. That is, the book itself is not subject to the laws of physics. Further clarification: if a human wants to read the book, they just reach out and grab a copy out of thin air, and put it back into thin air or onto a bookshelf when they are done.
5. No other book meets this criteria.

While this wouldn't prove that the book was written by an omniscient, omnipotent being that created the universe, it would definitely prove that the book is not written by man. So it's written by a being that is at least godlike.

An edit, based on muz's comment. It occurs to me that the questioner mentions "a god" as opposed to "God". In that case I suppose we could have many such books, and the best way for a rational person to be convinced that it was written by a god would be for the god to claim credit. For example, if there actually were an Athena and her powers and attributes were sufficient to demonstrate her godlike nature, then if she appeared on the Daily Show to promote her book, there wouldn't be a rational reason to doubt that she wrote it.

My first answer is based on the assumption that the book itself has to be proof of the existence of the god in question.

A further edit in response to sehe's comment. The properties I'm listing in my first answer are not properties of an intangible thing, or forces of nature like gravity. I'm saying that in order for a book to convince a rational person that it was written by a god, the book itself--the thing written on parchment, stone tablets, clay, or other media--would have to have those properties. I'm saying that if I wanted to read part of the Book, I would have to be able to reach out into thin air and conjure a copy of the Book, and that I couldn't conjure any other book. That's criteria 4. Criteria 3 means that whenever humans discuss the book, they agree. No exceptions, not even between teenagers and parents.

The book is also a source of unlimited electrical power, because it can be conjured and burned indefinitely, but depending on the contents people might or might not do this.

The book itself would have to have the following properties:

1. The book has always existed in every human culture.
2. Everyone can read it, whether they know how to read or not.
3. The book is clear and unambiguous on every point, and everyone who reads it agrees that this is so.
4. The book is not published by any known human agent, but it exists anyway, and no human is ever unable to obtain a copy. That is, the book itself is not subject to the laws of physics.
5. No other book meets this criteria.

While this wouldn't prove that the book was written by an omniscient, omnipotent being that created the universe, it would definitely prove that the book is not written by man. So it's written by a being that is at least godlike.

The book itself would have to have the following properties:

1. The book has always existed in every human culture.
2. Everyone can read it, whether they know how to read or not.
3. The book is clear and unambiguous on every point, and everyone who reads it agrees that this is so.
4. The book is not published by any known human agent, but it exists anyway, and no human is ever unable to obtain a copy. That is, the book itself is not subject to the laws of physics.
5. No other book meets this criteria.

While this wouldn't prove that the book was written by an omniscient, omnipotent being that created the universe, it would definitely prove that the book is not written by man. So it's written by a being that is at least godlike.

An edit, based on muz's comment. It occurs to me that the questioner mentions "a god" as opposed to "God". In that case I suppose we could have many such books, and the best way for a rational person to be convinced that it was written by a god would be for the god to claim credit. For example, if there actually were an Athena and her powers and attributes were sufficient to demonstrate her godlike nature, then if she appeared on the Daily Show to promote her book, there wouldn't be a rational reason to doubt that she wrote it.

My first answer is based on the assumption that the book itself has to be proof of the existence of the god in question.