A mei tai is a great suggestion. With newborns you need something that will still support their head and spine so you can't just pop them in an ordinary old front pack.
That said, I have a
Manduca which can be used to carry newborns, although I only got it recently so haven't used the infant insert part yet. I love it, might be worth a go if you're after something a bit more structured. (Other options are a
Beco or an
Ergo with an infant insert.)
Slingbabies are on Facebook too, could be a good idea to have a flick through the photo album to see what you like the look of...