Hello

Yes you might get a few good colleges under AYUSH AIQ with this rank including Chaudhary Harchand Singh Atmaram Education Trust, Quadra Institute of Ayurveda, Roorkee, Uttarakhand

Vinayaka Missions Homoeopathic Medical College, Salem, Tamil Nadu

Bharateeya Sanskriti Prabodhinis Gomantak Ayurveda Mahavidyalaya and Research Centre, Ponda, Goa

Alvas Ayurveda Medical College, Mangalore, Karnataka

National College of Ayurved, Hisar, Haryana

Father Muller Homoeopathic Medical College and Hospital, Mangalore, Karnataka

Solan Homoeopathic Medical college and Hospital, Solan, Himachal Pradesh  and many more but all under AQP (All India Quota Private) and MNG (Management Quota). I am not quite sure if you can get admission in Nagarcoil GOvt College but I insist you to go to https://medicine.careers360.com/articles/admission-ayush-courses-through-neet

for more details. All the best!