You can order it onsite, but all the planets would have to be in perfect alignment for there to be any advantage to doing that.
Whether there would be any advantage at all would depend on the exact date you order the card, and the exact dates of any future visits. Unless ordering at a particular time would give you DDE coverage for an extra trip...what's the point?
Also, ordering the DDE onsite can be additional steps during one of the busiest parts of you visit...arrival. So -- although I considered ordering it onsite -- I chose to order it a little ahead of time, just to get one more detail out of the way. I DID time the ordering so we'll probably get three trips, but I ordered about a month ahead from home.
Incidentally, we also paid for our card in just a couple of days, and we still had 12 1/2 months left on the card!
I have to say, though, that when it comes to renewal we will NOT get the extra card. It's great when it's for free, but paying $25 extra for the second card is just price gouging which offers little benefit for us.