I don't have bunnies, but I do have cats and have used some of these ideas in the past. They should work with dogs/puppies but beware of the chewing factor with puppies.

Note, the author suggests putting the damp sheet/pillow case over the pen/cage. The cats didn't and don't live in pens, so I draped the sheet over two plastic chairs. They seemed to like their fort and spent the hot part of the day inside it.

I know puppies, okay dogs were inclined to eat the plastic bottles. Instead of bottles I froze 'bricks of ice' in cottage cheese containers and plastic butter dishes. The dogs got the ice not the plastic. You might want to time how long each size lasts.

I also got a wading pool and filled it with ice when we arrived before the electricity was turned on.

Other than that I haven't tested these.