I agree with Mike - you will be struggling to find an indigenous tree that flowers year round. However, can I plea that you don't plant Banksia integrifolia (if that is where your line of inquiry is going). It has far exceeded Mike's statement of 'becoming a weed in some places' as it now found wild throughout the North Island (including Great Barrier Island) and it is starting to naturalise in the South Island. In some parts of the North Island - in parts of Northland, Coromandel, Bay of Plenty and the Manawatu for example we are now seeing it form dune forest. If you wish to plant a Banksia that does the same try Banksia serrata - it has only been found once naturalising and then poorly so.