I'm pretty vanilla when it comes to this. I like the standard 'diaper'. Sometimes I like to day pull ups if I wear pull ups. If I feel cute or naughty , I would use diapee. If I'm in a British mood, I would use nappy.
I think "diaper" is just an all-around fantastic and aesthetically pleasing word. I haven't come across a preferable alternative. It might be because I'm American, but "nappy" has never quite sat well with me, and I could never get the hang of calling them "dips". "Diaps", maybe, but not "dips".