Have a look at the following screenshot taken by me at Godaddy India to check the payment optionsavailable for Indian Customers-
So Personally I recommend Godaddy for new fresh Domain Name Registration or Domain Transfer to Godaddy, even you can use other Web Hosting Services like Bluehost & HostGator.
Visit Godaddy India Server - in.godaddy.com
Godaddy Customer Care Center Contact Numbers-
Toll Free - 1800 121 0111
Lines are open Monday-Saturday, 11 a.m. – 6 p.m. IST (closed Sundays)
Direct Contact to Customer Support India Team - 040-49187600 (Hyderabad)