I have a BB which apparently is good for newborns as well but my family has been telling me that babies up to 3 months HAVE to be placed flat all the time.. and that such carriers will damage my babies spine. He is almost 5 weeks now.
If he doens't like wraps have you tried a Mei Tai they are a similar sort of design as BB but soft structured so much better for their spine plus usually far more comfortable for you to wear. This website has good info on the subject plus many different types. [[ http://www.bigmamaslings.co.uk/zen-cart/soft-carri ers-tieon-soft-carriers-c-10_99_97.html]]
If he hate the kari- me. Don't buy anything unless you can borrow one from a friend to try it. The Kari -me is much more comfortable than the baby bjorne. You may just need to practise and try a time when he is calm and happy and doesn't need a feed.
What carry have you tried in the kari-me? DS always hated the cradle carry but loved the "newborn hug hold". I don't see the harm in trying the baby bjorn if you already have one. They aren't great for spinal position but the benefits of being carried are greater than the risks if it's your only option IYSWIM.
The baby bjorn won't be very comfortable for long though - maybe if he likes that, you could try doing a similar carry with the kari-me, which is more supportive for you both. (and supports correct spine position)