Hello,
Yes, Manipal University accepts NIOS student for Bsc in exercise and sport science course. As NIOS is a recognized board and it comes under Union Government of India. The minimum eligibilty criteria for the course is Pass in 10+2 or equivalent with Physics, Chemistry and English with Biology / Mathematics from a recognized Board, with minimum 50% aggregate marks or equivalent in PCB/PCM. And admission is given on the basis of merit cum basis, which score is higher of PCM/PCB.
If you fit this eligibilty criteria then you can apply for the course.

I hope this helps you.
All the best !!