I checked the airlines that offer magazine/newspaper redemptions (DL, CO, NW) and I didn't see any that offered the New York Times. The only dailies/weeklies available are Wall street Journal, Financial Times, The Economist, Newsweek, and Time.

If you really want to use your points for New York Times, I suppose you could redeem for an Amex gift card and then use that to pay for a subscription directly from the NYT. Or, try searching ebay for discount subscriptions; I've often had luck with cheap mags on there.