Generally speaking, a Certificate of Eligibility (CoE) is a document that must be obtained from the immigration authorities in Japan as a prerequisite for obtaining most types of long-term Japan visas (though exceptions exist).
In your case, the page about long-term visas on the website of the Embassy of Japan in India states
When an application for visa is made for the purpose of employment, residency, etc. in Japan, it is necessary for a proxy in Japan to obtain the “Certificate of Eligibility” and for the visa applicant to file a visa application to the Japanese embassy/consulate-general by submitting the original copy of the Certificate of Eligibility.
This is clearly not restricted to cases where the visa applicant intends to work in Japan, and applies to all types of visas for a long-term stay. So yes, a "proxy in Japan" (i.e., you) must apply for a CoE on her behalf, as described here.