No idea about private Universities in MP but i could suggest you some well known Private Institutes and Universities in India are as follow:
Birla Institute of Technology and Science (BITS), Pilani
Birla Institute of Technology (BIT), Mesra (Ranchi)
International Institute of Information Technology (IIIT), Hyderabad
Lovely Professional University, Punjab
Jawaharlal Nehru Technology University (JNTUH) Coll of Engg., Hyderabad
Manipal Inst. of Tech., Manipal
Thapar University, Patiala
Inst. of Tech, Nirma University
PES Inst. of Tech., Bangalore
National Institute of Engineering (NIE), Mysore