Digital Media market is grooming very high in India. Below are some of the major domains of digital media marketing:

Search Engine Optimization (SEO)
Search Engine Marketing (SEM)
Social Media Marketing (SMM)
Email Marketing
Inbound Marketing
Content Marketing
Affiliate Marketing
Mobile Marketing
Internet Marketing

Below I am providing you the list of institutes which provides courses on digital media marketing:

1 Digital Vidya:

This institute headquartered in Delhi and provides one of the most sought after course offered by Digital Vidya is Certified Digital Marketing Master Course (CDMM) which is a 6-month (with option to completed in 3 months) training program.

2 Digital Academy India

Yet another digital marketing training course offerer situated in the capital city of the country Delhi:

Digital Marketing courses are offered by Digital Academy India:

Certification Programme in Digital Marketing (CPDM)
Corporate Digital Marketing Training Programme

3 Digital Marketing Academy

Digital Marketing Academy is a Hyderabad-based digital marketing institute that offers the following set of courses:

Digital Marketing In-Depth
Search Engine Optimization (SEO)
Social Media Optimization (SMO)
Google Ad words/PPC/Search Engine Marketing (SEM)

Other institutes are:

NIIT
All India Management Association (AIMA)
Edukart
Webnext Solutions
Learning Catalyst