I was reading a book, while drinking (having) some coffee, would be the best way to say it. Switching the clauses also works, and sounds quite natural. The first sentence, "I was reading a book with having some coffee," is not right because you wouldn't say "with having." You could say "...a book, with coffee," but it wouldn't be quite right. "I was reading a book, having coffee," is just fine, but it sounds a little incomplete, like the sentence would go on after that (e.g. I was reading a book, having some coffee, when a raccoon ran in the door wearing a top hat.) "I was reading a book and had some coffee," sounds alright, but it sort of implies that you had the coffee later, or that you had it with you but weren't drinking it.

The most natural would be: - I was reading a book while/whilst having some coffee (or "While I was having some having coffee, I was reading a book"). -I was reading a book as I was having some coffee (or "As I was having some coffee, I was reading a book"). I was reading a book with having some coffee. - Incorrect I was reading a book, having some coffee. -Extremely awkward. You would never hear this except in poetry. I was reading a book and had some coffee - Incorrect, because the tenses don't match I was reading a book and having some coffee - Correct I read a book and had some coffee -Correct