OK, first up, Arlo's website has the 'official' chords on it.

http://www.arlo.net/resources/tablature/display.php?file=ring-around.chopro

But speaking as a rank novice, I found the D minor to B flat chord switch was a 
tad tricky which was a shame as this song's a real crowd pleaser!

Anyway, I found a way to cheat a bit and make the whole thing more novice friendly 
- transpose the chords down 5 semitones and capo it to the 5th fret to get it back 
into key.  It makes the chords way easier to play!

   C (x32010@1)               E71) (020130@1)I had a friend, a friend you could trust
Am (x02210@1)          F (133211@1)         
Went into the park and got busted
C (x32010@1)       D7 (xx0212@1)               G7Doin' (320001@1)the Ring-Around-A-Rosy-Rag.
C (x32010@1)               E7Went (020130@1)to the park, late at night
Am (x02210@1)                      F (133211@1)          
Ring-Around-A-Rosy in the middle of the night
        C (x32010@1)               D7 (xx0212@1)          G7 (320001@1) C (x32010@1)  G7 (320001@1)Yes, we all should do the Ring-Around-A-Rosy-Rag

Ch) Ring around, ring around Rose
Touch your nose and blow your toes
And mind after doin' the Ring-Around-A-Rosy-Rag.
Ring around, ring around Rose
Touch your nose and blow your toes
And mind after doin' the Ring-Around-A-Rosy-Rag.

2) We ought to send Officer Joe Strange
To some Australian mountain range
So we all could do the Ring-Aroud-A-Rosy-Rag
Would you like to put Philadelphia upthight, one mass
Ring-Aroud-A-Rosy in the middle of the night
Yes, we all should do the Ring-Aroud-A-Rosy-Rag

Ch)
C (x32010@1)        E7 (020130@1)     A7Touch (x02020@1)your nose and blow your toes
    D7 (xx0212@1)                 G7And (320001@1)mind after doin' the Ring-Around-A-Rosy-Rag.

Chords:
C     x-3-2-0-1-0
E7    0-2-0-1-0-0
Am    x-0-2-2-1-0
F     x-x-3-2-1-1
D7    x-x-0-2-1-2
G7    3-2-0-0-0-1
A7    x-0-2-0-2-0