You will only be able to electronically file your state return if you e-filed your initial federal and state returns. Please see this link for more information. If you did electronically file your original return and first amendment but are not being allowed to e-file again, you would need to mail in your amended return.
The amended boxes on IT-204, Section 1, question C, and the box on the New York Schedule K-1 will need to be marked as amended to file your partnership return accurately.
If this applies to you, please see page 3 and 4 from this link for guidance on where to mail your second amended return to New York.