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First of all, none of the local certificates are accepted for job as an HR generalist
HR generalist role normally have careers in small and medium enterprises where an individual handles multiple gamuts of HR function. It includes handling recruitment, employee relations, employee engagement, maintaining training records, handling HR operational roles, formulating, implementing and executing HR policies
To be honest, none of such professional institute exists and you will waste your money only.
However, you may invest in NHRDN and SHRM membership and gain such generalist experience one by one. Nobody can remain HR generalist in life, somewhere they have to pick up a higher role and handle specialised responsibilities.
As of now, the globally accepted qualification is SPHR membership which is costly but globally recognized. You may think about it

Hi,
There is no restriction on distance learning degree.
Ideally, to pursue a full time MBA, even from most reputed university, you should a graduate from a UGC recognized university. However you need to satisfy following criteria
1. The degree should have been awarded as per the UGC standard and guideline for awarding first degree
2. The degree should be of minimum 3 years duration
3. You should have minimum 50% in graduation if you are from open category and 45% if you are from SC, ST OBC category
4. The distance learning degree should have been awarded without violating territorial jurisdiction
for details please read following article
www.bit.ly/16BUeaM
I hope your query stands resolved
once you satisfy above, you have to appear for entrance exams like CAT, MAT, XAT, CET, GMAT and institute level entrance exam