What tense do you 'feel' the diary? There's no rule in anything like this, you just go with your gut feeling.
Past or present, first or third person, all have their advantages, drawbacks and difficulties. However, the latter are not insurmountable if you intend to publish.
If you do intend to publish, still go with your heart and don't just write to 'convention' or 'to the market'. You're going to be with this project for a long time and you'll need to love it as much as you love your baby. As someone once said to me, if you don't love it, how can you expect anyone else to?