If I could have an ideal carnival in the game, here's what I would had put in...
* Games: Or course. Play games to win many a furniture object, or even a rare hat or accessory. Maybe they're rare? Maybe it's a plushie version of Isabelle or Tom Nook? Probably it's a toy goldfish, perhaps? Maybe even a game console?
* Face Painting: Basically, have your face design with a wacky design. Want a furniture leaf on the side of your face? Consider it done. A Pitfall? Go for it. Heck, even go for both sides of your face if you desire! You can also go for a full face design. It won't wash away unless you take a dive or if you rub it off via either a wet wipe or tapping on a mirror somewhere and rubbing it off with a stylus. Cute your mayor even further with an awesome face paint design!
* Hats, Masks, Accessories, Back Items, etc: Want something new to decorate your head with? Then browse the various rare hats and caps they've got. Painting your face ain't your thing? Then go for a mask, instead! They'll probably be rare, but not like the prize hats which are more rare. They may even sell balloons, fans, pinwheels...
* Fireworks: Self-Explanatory. We all seen the sky blow up colorfully by now.
There may also be some more ideas, such as guessing how many jellybeans are in a jar, certain kinds of raffles...