This is exactly how the Dubliners play it, without a capo.
Basically the whole song just goes D A.

Intro (flutes): D A A D x4

VERSE I:
--------
       D             A
In the days I went a courtin',
      A             D
I was never tired resortin'.
      D              A
To an ale house or a playhouse,
    A                  D
And many's the house besides
      D               A
But I told me brother Seamus,
       A                D
I'd go off and be right famous,
      D             A
And I never would return again,
        A           D
Until I roamed the worldwide.


CHORUS:
-------
D                  A
Goodbye, Muirsheen Durkin,
         A                 D
Sure I'm sick and tired of workin'
   D                 A
No more I'll dig for praties,
       A              D
And no longer I'll be fooled
   D                  A
As sure as me name is Carney,
        A          D
I'll be off to Californy
         D               A
Where instead of digging praties,
        A                D
I'll be digging lumps of gold.


Inst. (flutes): D A A D x1


VERSE II:
---------
     D                A
I've courted girls in Blarney,
      A           D
in Kanturk and in Killarney
                  A           
In passage and in Queenstown, 
     A              D
that is the Cobh of Cork.
    D               A
Goodbye to all this pleasure,
        A              D
I'll be off to take me leisure
        D                     A
And the next time that you'll hear from me, 
          A               D
will be a letter from New York.


CHORUS:
-------
D                  A
Goodbye, Muirsheen Durkin,
    A                 D
I'm sick and tired of workin'
                     A
No more I'll dig for praties,
       A              D
And no longer I'll be fooled
                      A
As sure as me name is Carney,
        A          D
I'll be off to Californy
                         A
Where instead of digging praties,
        A                D
I'll be digging lumps of gold.


VERSE III:
----------
D              A
Goodbye to the girls at home,
    A                    D
I'm going far across the foam.
   D               A
To try and make me fortune,
   A        D
in far Amerikay.
        D                   A
There's gold and jewels and plenty,
        A                A
For the poor and for the gentry
    D             A      
And when I return again, 
  A               D
I never more will say:


CHORUS:
-------
D                  A
Goodbye, Muirsheen Durkin,
         A                 D
Sure I'm sick and tired of workin'
   D                 A
No more I'll dig for praties,
       A              D
And no longer I'll be fooled
   D                  A
As sure as me name is Carney,
        A          D
I'll be off to Californy
         D               A
Where instead of digging praties,
        A                D
I'll be digging lumps of gold.


Inst.: D A A D to fadeout.