Under what are you trying to petition? If you are trying to petition for a Green Card under family based immigration, then as far as aware you are unable to do so. Family based petitions are for those wishing to bring over spouses, children and parents. Nieces, nephews, cousins etc do not fall into this category. The only person who could sponsor your niece would be your sister when she becomes a US citizen (Im assuming that she isnt one as you are the one wanting to make the petition) or a spouse.
