There are many universities/colleges available but it would be better if you could share which particular state you are focusing on. Also, to check common colleges/universities you can go through the below names -
LOYOLA COLLEGE, CHENNAI
CHRIST UNIVERSITY, BANGALORE,
PRESIDENCY COLLEGE, CHENNAI
MADRAS CHRISTIAN COLLEGE [MCC],CHENNAI
Periyar University - School of Professional Studies, Salem
Jawaharlal Nehru University : Zakir Husain Centre for Educational Studies, New Delhi
Kurukshetra University : Department of Education, Kurukshetra
Pacific University : Faculty of Education, Udaipur etc.

Hope this helps!!!

Hi, There are various universities for Mphil you can apply in like:

LPU CP, Delhi
LPU Jalandhar
MMU Mulana
Amity university

You can check their official site for more details.

Good Luck!