The names some of the good schools in Chennai as your cousin want to admit her children in it are as follows:

Padma Seshadri Bala Bhawan Senior Secondary School, Nungambakkam, Chennai
DAV Boys Senior Secondary School, Chennai
SBOA School and Junior College, Annanagar, Chennai
Sishya School, Adyar, Chennai
The School KFI, Adyar, Chennai
P S Senior Secondary School, Chennai
Kendriya Vidyalaya – IIT Madras, Chennai
Don Bosco, Egmore, Chennai
The Ashram, Chennai
Vidya Mandir Senior Secondary School, Chennai
Chettinad Vidyashram, Chennai
PSBB Millennium School, Chennai
Bharatiya Vidya Bhavan, Chennai
Sacred Heart Marticulation High School, Churchpark, Chennai
Holy Angels Matriculation Higher Sec. School, Mogappari, Chennai
Good Shepherd High School, Nungambakkam, Chennai