I got a friend to help me set up a pair of keys. We set them up using my server (OS X) and copied the private key over. Apparently the permissions are the tricky part.

Here's my command:
rsync -au --delete username@server:/users/username/Dropbox /media/mmc1/Dropbox/

Of course, I had to create a Dropbox folder on my removable card and make sure there was enough room in the first place. I didn't mess with the -v flag since I'm hoping to do this in the background and don't need regular feedback (-v is for verbose), but I may add it back if I run into trouble. I added --delete to remove from the n810 anything that I've deleted from my Dropbox. I just installed WiFi Connection Manager on the n810, and plan to set it up to run that command whenever I join either my home or work network, since I'd like changes I make at one location to sync when I get to the other.

Thanks everyone for your help. I effectively have Dropbox on my internet tablet now!