Downvoting of comments already exists in the code; each user is prevented from downvoting until that user accumulates enough karma. I don't have the source in front of me, but you could set the threshold for that to 1, so users would be able to downvote comments as soon as they register.
Downvoting submissions is another story. As far as I know, HN has never let users downvote submissions, so you'd have to build in that scaffolding yourself.
