Yes there are courses on sports coaching available in many institutes in India. To be a sports coach ,one should not only have a degree but also should be physically fit and  Some of the institutes to pursue sports coaching are :
1. Netaji Subhash National institute of Sports ,Punjab offers a diploma course in Sports coaching and master of science in sports coaching also. The fee for the master degree is ₹9275 and one must have a minimum Percentage of 60% in graduate degree to be eligible for this post. The selection for the diploma course is based on different eligibilities such as  educational qualification ,sports achievements,performance in entrance tests and for northeast candidates also. One criteria of eligibility is if your educational qualification is graduation and you have participated in major international tournaments or recognised national tournaments or two times participation in university or junior championships,then your are eligible to write entrance tests for the diploma course.
If your educational qualification is sports achievement is 10+2 with participation in Olympic or commonwealth or Asian games then you are also eligible for entrance test for the diploma course of one year. The entrance tests is followed by Physical fitness test and personal interview. The total fee is ₹ 67,500 for the diploma course . Age must be 23 to 35 years .
2. National Sports East Centre ,Kolkata also offers a diploma in Sports Coaching.
Similar to the diploma course offeres by Netaji Subhash National Institute  of Sports ,one must be eligible based on our educational qualifications or personal achievement in sports with graduation  at national or international level or two times participation at national level games for a qualifications of 10+2 only.The fee for the diploma course is ₹67500  and duration is for one year . the age requirement is that you must be between 23 to 35 years of age . If you are eligible and fulfills the criteria then you can write the entrance test followed by Physical fitness test and personal interview .
3. National Sports West Centre,Gujarat also offers a diploma in Sports Coaching. This institute also has an entrance test followed by Physical fitness test and interview . They also have different eligibility criteria like  for graduation,one must have a sport achievement such as participation in international recognised tournament , participation in national recognised tournaments and two times participation in National junior championship or university championships . For 10+2 ,sports achievement must be in Olympic games or Commonwealth games or Asian games . The total amount for the fee is ₹67,500.
4. Lakshmibai National Institute of Physical Education also offers a diploma in sports coaching. To be eligible ,one must have passed 10+2  and one must have been deputed to the course by Defence or Army sports control board. The total fee is around ₹31000 per semester.

Not only a diploma course can get you into sports coaching  but there are also  many institutions in India offering degrees in Physical Education  through which one can enter careers of sports coaching . Some of the top colleges for physical education are:

1. Indira Gandhi Institute of Physical Education and Sports Science also offers Bachelor of Science in Physical Education and Sports. It is for a duration of one year and one must be a  graduate to be eligible for the course .feel structure is ₹8576.

2.  Lakshmibai National Institute of Physical Education, Thiruvananthapuram:
It is one of the top institutes providing Bachelor in Physical Education. The eligibility is different based on the educational qualification and achievements. To be eligible ,you must have a degree in any branch with 45% aggregate and achievement in sports such as participation in university ,district ,national or international ,state championships. Selection is through written test, Physical fitness test, sports proficiency test and achievements also contribute. The merit list are then selected based on the tests. The fee for B.P.Ed is ₹39,000 per semester.
3. Lakshmibai National  Institute  of Physical Education ,Gwalior also offers a Bachelor in Physical Education with direct admission provision for candidates who has participated in international championships, commonwealth and Asian games. There is written and physical fitness test for the entrance exam . One must also have passed 10+2 with minimum 50% aggregate . Fee is around ₹30000 for each semester.