I would like to know what annual...

Japanese beetles prefer perennials, and they do their dining on leaves, not flowers. Try planting marigolds, cosmos, bachelor’s buttons, and morning glories. Stay away from yellow flowers (with the exception of marigolds) — yellow is their favorite color. If you find them to be a problem in your garden, head out first thing in the morning with a bucket of soapy water. Getting rid of the beetles is as simple as shaking them into the bucket.