Usual ones are "Dee", "Di" and "DeeDee". Other options are "Anna", "Annie" and "Danni". "Dinah" might be amusing once or twice, but be careful--it could become unwelcome if it sticks.
I like "Jenna" all by itself, and the only two logical diminutives are "Jenny" and "Jen", I think. By habit, you will find yourself using "Jen" a lot, I'd wager.