Not authentic Hawaiian, but I just love "My Little Grass Shack in Kealakekua, Hawaii," because it's so much fun to sing
"Homo mai no ka'ua i ka hale wela ke hau (sp?)
and
"humu-humu nuku=nuku a pua'a"*

*Hawaii's state fish, I am told.

I also like the Hawaiian version of the newer version of Hawaiian Wedding Song. (There is an older, more 'authentic' Hawaiian song on which the popular song was based.)

 Hawaiian Wedding Song
  
  This is the moment I've waited for;
   E   - i  -a a - u   ke  ka-li  nei 
  
  I can hear my heart singing;
   A    i-a   la    i    he-a 
  
  Soon bells will be ringing
  Ku -   u     a  --- lo   - ha.
  
  This is the moment of sweet aloha.
   E -  i - a   a-u   ke hu-li  ne-i.
  
  I  will love you longer than forever.
   A   lo - a  - a   a - e   ka  ma-na-o 
  
  Promise me that you will leave me   never.
   Ma - ha ka  i  -  i - ni   a   ka  pu-u-wai.
  
  Here and now, dear, all my love  I  vow, dear.
   U   -  a      si  -  la  pa - a  ia  me   o - e 
  
  Promise me that you will leave me never.
   Ko  a - lo - ha ma - ka   mae   e i-po 
  
  I will love you longer than for-ever.
   Ka'u    ia   e  le - i  a - e ne-i-la 
  
  Now that we are one, Clouds won't hide the sun.
  Nou  no  ka i - ini    A    nou    wa - le  no 
  
  Blue skies  of  Hawaii  smile
  A     o     ko  a-lo-ha  ka'u 
  
  On this, our  wed-ding    day.
   E   hi  - i  - po - li   mau 
  
  I     do   love you   With all my heart.
  Na'u  oe    e   lei,  na'u oe  e  lei.

I doubt that the English words correspond closely in meaning to the Hawaiian ones. I just put them in to show metric correspondence. However, my spacing between words may disappear when I post this, so it may not work.

Genie