I just canceled my NYT subscription based on this comment. I was able to do so by logging into my account, following the "Cancel" link, then choosing the online chat option. It wasn't as easy as an automatic cancellation, but it wasn't terrible. Here's the transcript:
Isaiah: Hello Jay and thank you for contacting The New York Times! My name is Isaiah and I will be able to make any changes to your account today! One moment while I pull up your account.
Isaiah: I have located your digital account and I would like to personally thank you for being a Basic digital subscriber with the account number (XXXXXXXX)
Isaiah: If you don't mind me asking, what led you to cancel? I would love to gain your insight and see if there are any potential issues that I may resolve for you.
Jay: Please cancel my subscription.
Isaiah: May I ask why you wish to cancel?
Jay: I decline to answer that. Please cancel my subscription.
Isaiah: please note that leaving will put you back at 5 free articles per month and you will no longer have unlimited access to our content. Any saved Cooking recipes will stay saved but you will not be able to view them until you subscribe again.
Jay: I understand. Please cancel my subscription.
Isaiah: I understand your concerns. Because your readership is important to us, I'd like to extend a special offer for $2 per week for 1 year.
Jay: No thank you. Please cancel my subscription.
Isaiah: You will continue to enjoy all your subscription benefits for the rest of your billing cycle, which ends on February 07, 2019. Unfortunately we cannot issue any credits or refunds for the remainder of this billing cycle.