Obviously you can sponsor for a nanny from Nepal. But I think you asked a wrong question. The right question would be 'can the person get a visa?'
Give it a try and lets us know how it goes so that all other people might take benefit from your experience.
Documents you might be needing:
1. w2 from last 2-3 years
2. An invitation letter to the person stating her monthly or weekly salary, assurance of what kind of health insurance you will provide your nanny during her stay in the USA with you. Also write down what kind of other benefits you will provide.
3. Sponsorship letter to the embassy/consulat
4. Proof that you made enough search to find a nanny in the USA
5. Proof that you did not find a right person, and a good logic on why you could not trust a person in the USA to take care of your son. Remember, there are several thousands people in the USA who have nanny from the USA.
6. Application for Visa (the person in Nepal has to file)
7. Passport of the person
8. Your notarized copy of green card
9. Notarized copy of your Social Security card ( it might not be needed as well, but good to have)
10. Copy of any other form of your identification, like, driver's license, state identity card etc
11. Your lease agreement of your apartment. Understand, you need to show that you have enough room for your family and a separate room available for your nanny to live. If you have house, show the documents.
12. Your current pay stuffs. You should be able to show 2 months of your pay stuffs and should be able to prove that you make enough income to support your family and nanny as well as be able to pay your nanny her salary.
13. Good to have if your nanny is already licensed back in Nepal or have taken some kind of training on taking care of babies or elderly person or a disabled person. If she has any certificate or license or experience letter, that helps.
14. Lastly, please contact a lawyer over here to understand what kind of documents are needed and what kind of application is needed, what kind of visa is needed.
Note: I am not a lawyer. Also, I never sponsored any one for nanny. But I have seen a white couple sponsoring a Filipina from the Philippines. However, they were US citizens, not GC holder like you.
