What is the ruling on one who swore by the Book of Allah that he did not know his wife caused the death of his child, with blood around the child's nose, and is expiation obligatory upon him, and is it obligatory for his wife to fast for sixty days or pay a reduced blood money along with fasting for two consecutive months?

It is impermissible to swear an oath except upon the truth. However, it is permissible to lie in an oath if it is to avert certain harm that cannot be avoided otherwise. There is no sin in that, nor is expiation required. If the cause of the child's death was the mother unintentionally placing her hand over his nostrils, it is considered involuntary manslaughter, necessitating the blood money (diyah) from her 'aqilah (male agnatic relatives responsible for paying blood money) and expiation. The mother does not inherit from the blood money.