As far as service providers go there's Labindia (now part of Life Tech), Genotypic in Bangalore, Ocimum Biosolutions, and Xcelris Labs. The number of training institutes is large though coverage of NGS analysis may be spotty. Maybe this will help.
I am not sure whether your question about training institutes was also meant to include masters programs. But in any case Manipal University has a [?]bioinformatics masters[?] which is not specifically focused on next generation sequencing. We (Maastricht University) collaborate with them. We developed the curriculum together and Manipal students can do an [?]internship in Maastricht[?]. Four of them did so last year. [?]This poster[?] gives a nice impression about what they did.