The problem is handwriting; not as many apps do that, and most are for note taking.
One suggestion is Note Taker HD. It's one of the best note taking apps, and designed for handwriting. The cool thing is that it can shrink the handwriting down to fit, and you can include pictures or text as well. It can allow a PDF template, so it's like handwriting on a form. I didn't see a diary template, but they have day-week-month planners, storyboard, etc. You could probably make one. And you'd have to work out a scheme for dating them, but perhaps its tags function would work for that.
Another good choice is Penultimate, which is part of Evernote. I don't think it's as good as Note Taker HD for pure handwriting, but where it excels is in its integration with Evernote. And once the stuff is in Evernote it does OCR/handwriting recognition, and it's amazingly good. So your notes become searchable (and of course Evernote syncs with everything that has an operating system). It also does backgrounds, and has some templates for sale. And you'd have to set up some kind of a notebook with a dating scheme if you're using it as a diary, perhaps with tags. And once in Evernote you can add reminders, which is something you want.