Except when downloaded to iTunes, Apple's rentals cannot be played/moved on another device. The rental will work on your iPad only.
Best option would be to contact iTunes Store support and say you've had trouble downloading to iPad - hopefully they'll cancel the rental and give you the credit to enable rental on AppleTV.
I would also raise with them the stupidity of the service allowing you to rent a title when there is insufficient space on the iPad to download the movie in the first place!
I had the same problem just now. The solution is to attempt to rent the movie again, iTunes displays a message indicating you have already rented the movie and advises you to go to the Downloads section to manage your downloads. The movie should automatically start downloading and the Downloads menu option should appear alongside the Purchases menu option. It's not particularly obvious (Apple), but at least I could download the movie and watch it now.