Several thoughts:
I think they advertised in Kinnick that you can get the "question" posted on scoreboard and be on the corner of the field between qtrs (not sure about that part) for $250. Probably could get a pro photo thrown in by university. Pricey, but certainly memorable. contact the athletic office for directions.
You could secretly tape the ring to the underside of her seat, and make up something about some contest that they "just announced" (and she obviously didn't hear), that you have to check under your seat to see if you've won!
Also, There's a university volunteer student located under the "BIG blowup Herky" at the south end of stadium (on outside, by Melrose Ave, with Kinnick Stadium conveniently in background), who is specifically there to take photos of people with the blowup Herky using your own camera!
Or, secretly ask the guy selling programs who stands on a box behind a podium (there are a few of these stations located around main walkways next to stadium), to let you use the podium for a quick minute, then yell out to the world your intentions...could be creative, but kinda reaching there though.
A good backdrop for photo ops is the Football operations bldg where it says "Hawkeye Football" pretty prominently. Located on West side main parking lot at the North end. Good backdrop of Kinnick, in the opposite direction, there too.
Of course, There's always Joe's Place, Mickey's, The Column, Deadwood, etc to make it memorable!
Good Luck and Congratulations! (post back here and let us know how it went and if she said yes)