This depends in part on who officially owns the account.
Federally, 529 plan contributions are not tax-deductible, regardless of ownership. Anyone can contribute to a 529 plan, though; the earnings of the 529 plan are tax-deferred and are tax-free if they are used for qualified educational expenses.
In the state of New York, the account owner is entitled to deduct up to 10,000 (Married filing jointly) from their state taxes; however, that's limited to the account owner only. If they're not in the state of New York, they may be able to have similar benefits from their home state; check their rules.
You may have multiple accounts for one child, though, so if you and they both want to contribute for your child, that's perfectly fine. The limits are at the taxpayer level, so you can deduct $10k for all contributions to all children's accounts in sum (5k per kid if you have 2, and want to contribute equally, for example), but they can do the same.
Gift tax is the other relevant thing to consider. You can contribute $14k per year without either paying gift tax or adding it to the lifetime maximum (which is currently $1.5MM, but could change at any time either up or down). You can also make a one-time contribution of 70k (5 years' worth) and have that amount exempt as if it were contributed over five years.
For more information on all of this, see the New York 529 Page for more details.