Hello there,

Some of the private college in Tamil Nadu are:

• Amrita school of engineering, Coimbatore
• Bannari amman institute of technology, Erode
• Bharath institute of higher education and research, Chennai
• Hindustan institute of technology and science, Chennai
• Kalasalingam academy of research and education, Virudhunagar

For complete list of colleges in Tamil Nadu check the link below:

https://engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-tamil-nadu

Some of the private colleges in Kerala are:

• TKM college of engineering, Kollam
• Indian institute of information technology, Kottayam
• Mar Athanasius college of engineering, Kothamangalam
• NSS college of engineering, Palakkad
• Rajagiri school of engineering and technology, Kochi
• Mar baselios college of engineering and technology, Thiruvananthapuram

Hope this helps.

GOOD LUCK!!