The other versions don't sound right to me, so this is my try.

The Am, Am(maj7) and Am7 is basically a step down of the fourth string:

      Am     Am(maj7) Am7
e|----0-------0--------0-------|
B|----1-------1--------1-------|
G|----2-------1--------0-------|
D|----2-------2--------2-------|
A|----0-------0--------0-------|
E|----x-------x--------x-------|

The B7 can be played in various ways, I like the sound of this one:

e|----2---|
B|----0---|
G|----2---|
D|----1---|
A|----2---|
E|----x---|


  Am       Am(maj7)    Am7      Dm
  A gentle breeze from hushabye mountain

  F      Am         B7      E
  Softly blows o'er lullaby bay

  Am           Am(maj7) Am7            Dm
  It fills the sails of boats that are waiting

  F          Am        E      Am
  Waiting to sail your worries away

  
  Dm        B7        E 



  Am       Am(maj7) Am7      Dm
  It isn?t far to   hushabye mountain

  F        Am         B7          E
  And your boat waits down by the quay

  Am           Am(maj7)  Am7        Dm
  The winds of night so  softly are sighing

  F              Am       E           Am
  Soon they will fly your troubles to sea



  Dm            A       F        G
  So close your eyes on hushabye mountain

  Bb   Dm         B7            E
  Wave goodbye to cares of the day

      Am         Am(maj7)  Am7      Dm
  And Watch your boat from hushabye mountain

  F        Am        E       Am
  Sail far away from lullaby bay