I have read that the pronunciation of Canberra's name was to be decided by however Lady Denman pronounced it at the naming of Canberra ceremony held on the 12th March 1913.
I suppose the most common pronunciation for Canberra I have heard over the years from visitors is Can-ber-rah. Personally my family pronounced it as Can-brah. This article from 1926 concludes with the pronunciation as Canb'ra. Pretty close...
The Mercury - 1 May 1926
National Library of Australia