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 (x02210@1)     Am(maj7)    Am7 (x02010@1)    Dm (xx0231@1) A gentle breeze from hushabye mountain

F (133211@1)    Am (x02210@1)       B7 (x21202@1)    E (022100@1) Softly blows o'er lullaby bay

Am (x02210@1)         Am(maj7) Am7 (x02010@1)          Dm (xx0231@1) It fills the sails of boats that are waiting

F (133211@1)        Am (x02210@1)      E (022100@1)    Am (x02210@1) Waiting to sail your worries away

Dm (xx0231@1)      B7 (x21202@1)      E (022100@1)

Am (x02210@1)     Am(maj7) Am7 (x02010@1)    Dm (xx0231@1) It isn't far to   hushabye mountain

F (133211@1)      Am (x02210@1)       B7 (x21202@1)        E (022100@1) And your boat waits down by the quay

Am (x02210@1)         Am(maj7)  Am7 (x02010@1)      Dm (xx0231@1) The winds of night so  softly are sighing

F (133211@1)            Am (x02210@1)     E (022100@1)         Am (x02210@1) Soon they will fly your troubles to sea



Dm (xx0231@1)          A (x02220@1)     F (133211@1)      G (320003@1) So close your eyes on hushabye mountain

Bb (x1333x@1) Dm (xx0231@1)       B7 (x21202@1)          E (022100@1) Wave goodbye to cares of the day

Am (x02210@1)       Am(maj7)  Am7 (x02010@1)    Dm (xx0231@1) And Watch your boat from hushabye mountain

F (133211@1)      Am (x02210@1)      E (022100@1)     Am (x02210@1) Sail far away from lullaby bay