Hello Aspirant,
Some top private colleges for BAMS in India are enlisted below :-

Shree Guru Gobind Singh Tricentenary University, Gurgaon

Tilak Ayurved Mahavidyalaya, Pune

Patanjali Ayurved College, Haridwar

K G Mittal Ayurvedic College, Mumbai

JSSAMC Mysore - JSS Ayurveda Medical College

Ashtang Ayurved Mahavidyalaya, Pune

Sumatibhai Shah Ayurved Mahavidyalaya Malwadi, Pune

Bharati Vidyapeeth Deemed University College of Ayurved, Pune

Himalayiya Ayurvedic Medical College and Hospital, Dehradun

Sri Kalabyraveshwara Swamy Ayurvedic Medical College, Bangalore

Dr DY Patil University, Navi Mumbai

Vidarbha Ayurved Mahavidyalaya, Amravati

CSMSS Ayurved Mahavidayalya and Ruganalay, Aurangabad

For complete list refer to the link given below :-

https://medicine.careers360.com/colleges/list-of-medical-colleges-in-india?ownership=Private&degree=B.A.M.S.&branch=Ayurveda

I hope this information helps you.
Good Luck!!