He has a newborn in China who he wants to register as British. He has been declined a passport for her as you cannot apparently pass on British citizenship to the child of one who is British by descent.
They're correct. British citizens by descent cannot automatically pass British citizenship to a child born abroad. There are limited circumstances in which such a child can be registered as a British citizen while under 18:
If your son's parent (the child's grandparent) was a British citizen otherwise than by descent, and your son lived in the UK for some continuous period of 3 years some time in his life before the child's birth, the child can be registered as a British citizen by descent under section 3(2).
If your son and his wife and his child have all been living in the UK for the last 3 years, the child can be registered as a British citizen otherwise than by descent under section 3(5).
Under special circumstances, the Home Secretary has the power to register any child under 18 as a British citizen under section 3(1). This is usually for children who are already in the UK and have strong connections to the UK.
You may find this UK government webpage ("Check if you're a British citizen") useful to test your thoughts. It poses questions in order to determine British citizenship.
Better Answers contain actual text and substantive information, so the Answer remains useful if the link disappears. This issue's presentation on the UK website, however, has too many pages and conditions to easily quote or abstract.