Here is the main riff for lullaby, ive tabbed it a little differently but the 
sound is fuller in my version i think :)

Tell me what you think...
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Lullaby - Dixie chicks

        r      r            r        r
e|-------------------|---------------------|
G|-------------------|---------------------|
B|-------0-----------|-------0-------------|
D|----0-2-2-----0-2--|----0-2-2(0)----0----|
A|--3-0-3--3--3-0-3--|--3-0-3-3(0)--3-0-3--|
E|--1---------1------|--1-----------1------|

Slightly different version:

        r      r           r    r        r
e|---------------------|---------------------|
G|---------------------|---------------------|
B|-------0-------------|-------0----------5--|
D|--3-0-2-2---3-0-2(2)-|--3-0-2-2-0---3-0-5--|
A|--3-0-3--3--3-0-3(3)-|--3-0-3-3-----3-0-3--|
E|--1---------1--------|--1-----------1------|
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Chords:

e|-----------------|-----------------|-----------------||-----------------|
G|-----------------|-----------------|-----------------||-----------------|
B|-----------------|-----------------|-----------------||----------5***---|
D|--3--3-3--0-0-0--|--3--3-3--0***---|--3--3-3--0-0-0--||--3--3-3--5***---|
A|--3--3-3--2-2-2--|--3--3-3--2***---|--3--3-3--2-2-2--||--3--3-3--3***---|
E|--1--1-1--3-3-3--|--1--1-1--3***---|--1--1-1--3-3-3--||--1--1-1---------|
 

Or you can just use C and F alternatively 
                   |---|  |-1-|
                   |-1-|  |-1-|
                   |-0-|  |-2-|
                   |-2-|  |-3-|
                   |-3-|  |---|
                   |---|  |---|
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 r or * - let ring

( ) - strum quickly and quietly while letting ring,
      comes naturally when strumming, (not muted!)

 x  - muted