I did a little investigating with this one. There are at present several obstacles to the NYTimes app working on the edge:
1. It is allegedly built for Android 2.0+
2. It's not available outside the market
3. Even obtained through a device with market access, the apk is a "Protected App" and therefore cannot be backed up via astro and exported in the usual workaround. (at least, not unless your phone is rooted)
4. Even then, many apps obtained through the market are linked to a goggle account (especially protected ones, even if free) and if somehow circumvented, they may cease functioning when the device that the apk is put onto (like the edge) does not match that account.

That really stinks because I would have liked this app too. I'm going to do some further digging though to see if a solution can be worked out.

In the meantime though, I did find a way to get NYT articles for download and consumption as EPUB files that are readable on the eInk side. I use wizardrss.com to convert RSS links on NYT so they retrieve the full articles, then I use Feedbooks.com to make my own "newspaper" by adding those converted RSS feeds. Then whenever I want a fresh "newspaper," I log into feedbooks on the edge and just download the EPUB file (PDF is also available). The file is created from the most recent feeds at time of download, and the filename has a date marker.