I don't think that it is so much an issue of a specific book, as plainly obvious facts.
If the statement that secularists have no morality is true, then it should be obvious. Criminals should have a large majority of atheists, but as it turns out, ( at least in north america, maybe the stats are different elsewhere.) the opposite is true. Not that there are no atheists who commit crimes, but that the overwhelming majority of those committing crimes, is the same overwhelming majority that are not committing crimes. Religious folk.
I find when this argument is used, the standard tactic, once this is brought up, is that the person claiming it is going to start quoting bits of their holy book that are not necessarily moral ( merely instructions in said book, versus things that help, benefit, and generally keep society from crumbling. ) , gay marriage, worshiping god, etc.
Essentially they confuse what is moral with what is written in their book. And while their book may have some morality in it, not every instruction, story or parable within is what we would consider morality.
In short, they are messing about with the word morality.