It's mainly Bm, then F#MAJ, switches to a E at some point can't quite figure it out. But I am positive about the Bm and F# here is what I got with the lyrics

F#
You know that I am called the Count
Bm                      F#
Because I really love to count
E(?)
I could sit and count all day
F#
Sometimes I get carried away

       Bm                            F#
I count slowly, slowly, slowly getting faster
F#                                           Bm
Once I've started counting it's really hard to stop
Bm                      F#
Faster, faster. It is so exciting!
E(?)                                 F#
I could count forever, count until I drop

Bm             F#
1! 2! 1! 2! 3! 4!
E             F#
1-2-3-4, 1-2-3-4

(Repeat progression through out the rest of song)

I count the spiders on the wall...
I count the cobwebs in the hall...
I count the candles on the shelf...
When I'm alone, I count myself!

I count slowly, slowly, slowly getting faster
Once I've started counting it's really hard to stop
Faster, faster. It is so exciting!
I could count forever, count until I drop

1! 2! 3! 4!
1-2-3-4, 1-2-3-4, I love counting!
That's the song of the Count!