TEAM*

This group is the closest thing to Vampire Weekend that I've ever come across (other than Vampire Weekend themselves).  Overall they have a slightly more poppy sound, and a slightly less Caribbean flavour, but the use of vocals is very similar.  Here is a representative song.  And here's another one.  The vocals work really well with the backing instrumentation.  They have all their music on their bandcamp page.

Hollow Coves

This duo is from Brisbane.  They have a subdued, folky rock sound which I really like.  One of the guys sounds hard-core Australian, but the other sounds American.  I think the closest similarity I have heard is Angus and Julia Stone (incidentally also from Australia).  Check out this song, which seems to be one of their more popular ones.  It's actually my least favourite...I much prefer the other ones you can hear on their bandcamp.  I really like the guys' voices, and the subtle instrumentation which gradually builds during their songs.  "Heatwave" is my personal favourite.  I highly recommend checking out the group if you enjoy chill indie rock.