Binisha appears most common in
India and the near East (
https://www.linkedin.com/pub/dir/?first=binisha&last=&search=Search&searchType=fps and
http://www.name-list.net/facebook/firstname/Binisha) so it's origin may lie in that region... I can't find an meaning or origin for it anywhere though, but given it's likely region of origin, it's probably a variant of another, more common name. What, I'm not sure, but maybe someone else more familiar with those areas and the languages there could be of more help?
Sorry!
My PNL = http://www.behindthename.com/pnl/37275
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