What are the best ways to invite my brother's Christian wife to Islam, considering that she is currently not interested, despite repeated prayers for her and offering booklets, and her saying "Insha'Allah I will think about it" when the invitation is mentioned to her?

The best means of inviting to Islam are to supplicate for the one being invited, to convince them with rational arguments, and to soften their hearts with encouragement and deterrence, all while being kind to them and patient. It is a condition for marriage to a Kitābī woman (a woman from the People of the Book) that she be chaste and virtuous, based on the words of the Almighty: "This day [all] good foods have been made lawful for you. And the food of those who were given the Scripture is lawful for you, and your food is lawful for them. And [lawful in marriage are] the chaste women from among the believers and the chaste women from among those who were given the Scripture before you" (Al-Ma'idah: 5). One must protect her from anything that compromises morality and leads to the forbidden.