Going by previous All India cut offs and your cousin's rank, he may decent chances in:

MGM Medical College, Mumbai

Amrita Institute of Medical Sciences, Kerala

K.S.Hegde Medical Academy

KMC, Manipal

Yenepoy

Government College is tad difficult with this rank. Having said that, this is 2019 data and cut offs change every year depending on various factors such as no.of Candidates appearing for the exam, no.of Candidates qualified, difficulty of the exam, and no.of seats available for each specialisation. Please try our College predictor to check the possibility of other specialisations with you rank across India:  https://medicine.careers360.com/neet-pg-all-india-college-predictor