Dakshina Bharat Hindi Prachar Sabha

Why not? There are many universities running the same. In your vicinity, you can enroll yourself as a private student in any college affiliated to a university.

Contact them directly for guidance-
http://hindisabhatrichy.com/HTML/contact.html.

You need to fulfill the eligibility as below.
Age: Minimum 18 years
Candidates who have passed 10+2 or 10th +Visharad + Rashtrabhasha Praveen Pariksha or equivalent are eligible to apply.
If you tick all the boxes, then you surely can.
Still, you need to check with the college for reliable information.

Hi,
Admission to most of the colleges is closed. It is advisable to get in touch with the college officials for detailed information.

Hi,
It is advisable to get in touch with the college officials for such details:
http://www.dbhpscentral.org/contactus.html