Are there any organizations in New York City that assist with filling out the I-912 form?

The form is clear, and so are the instructions. You can only apply for fee waiver in very limited circumstances. Generally, your sponsor is required to provide for your needs if you cannot. If you meet the requirements to apply for fee waiver, then perhaps Catholic Charities can help you. However, you have to consider whether you want to disclose all of your personal and financial information to unrelated third parties. It's not exactly as confidential as you might prefer.

try catholic charities ..they have immigration help http://www.catholiccharitiesusa.org/
although that form is not very difficult