I recently sent an email to groupsubs@nytimes.com asking for the same information, and I got the below response.  It looks like a site license should be available the second quarter of this year.

Dan

Hello,

Thank you for your inquiry about digital subscriptions to NYTimes.com for educators and students. We can offer you the following choices now:

Individual digital subscription at the education rate: Visit NYTimes.com/CollegeRate or NYTimes.com/TeacherRate and save 50% on each of our three digital subscription options. To order at these special rates, you must have a valid college or school e-mail address. Rates begin at only $1.88 per week. Note: We do not offer a subscription to NYTimes.com only.
Group digital subscriptions at the education rate: We can bill you for subscriptions you wish to provide to specific individuals -- such as educators in your school or department. These subscriptions will be charged at the individual education rate. You must provide the school or college e-mail addresses for each individual included in the group subscription. For subscription options, rate and restrictions, please refer to NYTimes.com/CollegeRate orNYTimes.com/TeacherRate. If you have questions or wish to order a group subscription, please send an e-mail to edu@nytimes.com with “Group Subscription” in the subject line.

Seat licenses. With a seat license, a certain number of individuals in a specific IP range will be able to claim a “seat” each day for access to NYTimes.com. This will enable you to provide access for students, for example, as seat licenses do not require individual e-mail addresses. Access will be provided through a portal on your own Web site.
Site licenses. With a site license, everyone in a specific IP range will have access to NYTimes.com.