Yes, what I recommend is that you take what you owed as a balance this year to NY, and divide that by 4. That number will be what you should pay each quarter to NY directly as an "estimated tax payment." For example, if you needed to pay $4,000 with your tax return, then 1/4 of that is $1,000. You should pay $1,000 each quarter to NY for your estimated tax payment in this example.
Here is a link to the voucher you can mail in with a payment: IT-2105
