After you enter the 1099-MISC on the Federal return, you will subtract it from the New York state return using Form IT-225. This form IS supported in the TurboTax programs.
According to the State of New York:
"The State has released a new form in 2014, the IT-225. This form is used to report any NewYork additions and subtractions that do not have its own line in the IT-201. The LOSAP exemption is subtraction S-130. Since the State has created this new form, the federal tax form on which the LOSAP distribution is reported should not create any difficulty in taking this exemption."
Are you a full-year resident of New York?
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