Dear Atlanta Brother!
It seems the Indian Constitution does not permit dual citizenship. But the closest we can get to dual citizenship is with this OCI registration.
The 'Overseas Citizen of India' terminology is a misnomer, because the citizenship emphasis is on the 'Overseas' portion rather than on the 'India' portion of this term. But as an OCI, we get lifetime visa privileges and multiple-type visa privileges (we can work, tour, visit, literally do anything). The only things we cannot do that an Indian citizen can do are - to vote, be an MP/MLA, hold government jobs, and buy agricultural/plantation properties.
We used to have a PIO (Person of Indian Origin) Card that is similar to your NICOP. The PIO card's validity is 15 years. We still have that facility, but I do not know who will prefer the PIO to the new OCI card.
Regards,