There are many private colleges which offer civil engineering..

1.IIIT Hyderabad

2.VIT Vellore

3.Dhirubhai Ambani IICT Gandhinagar

4.PSG College of Technolongy Coimbatore

5.MIT Pune

6.NIE Mysore

7.Manipal Institute of Technology Karnataka

8.RV College Bengalore

There are many other too and to know about the entrances and other details visit the official websites of the respective colleges.

Here are some of the private Engineering colleges you can prefer given below:

Amrita School of Engineering, Coimbatore

Manipal Institute of Technology, Manipal

SRM University

VIT Vellore

Good Luck!