Below are the private colleges which are offering aerospace engineering

1- Amrita school of engineering
2- Manipal Institute
3- College of Engineering Studies, University of Petroleum and Energy Studies, Dehradun
4- Alliance College of Engineering and Design, Bangalore.
5- Birla Institute of Technology, Mesra

To check all the colleges which are offering aerospace engineering you can refer below link-

http://www.engineering.careers360.com/aerospace-engineering/colleges