Here are the chords, straight from the Master himself. I strongly recommend the Lehrer songbook. It's full of the most wonderful chord progressions, passing chords and the odd 'dim' here and there.
The Vatican Rag - Tom Lehrer
[G7]First you get down on your knees,
[C6]Fiddle with your rosaries,
[G7]Bow your head with great respect,
And [C]genu-[C#dim]flect, genu-[Dm]flect, genu-[G9]flect!
[G7]Do whatever steps you want if
[C6]You have cleared it with [Bb7-5]the Pon-[A7]tiff,
[F]Ev'rybody [F#dim]say his own
[D7]Doin' the [G7]Vatican [C]Rag.
[G7]Get in line in that processional,
[C]Step into that small confession-[C#dim]al,
[G7There the guy who's got religion'll
[C]Tell you if your sin's origi-[C7]nal.
[F]If it is, try playin, it safer,
[Fm]Drink the wine and chew the wafer,
[F#dim]Two, four, six, eight,
[G7]Time to transubstantiate!
So get down upon your knees,
Fiddle with your rosaries,
Bow your head with great respect,
And genuflect, genuflect, genuflect!
Make a cross on your abdomen,
When in Rome, do like a Roman,
Gee, it's good to see ya,
[D7]Gettin' ec-[G7]static an' [D7]sorta dra-[G7]matic an'
[D7]Doin' the [G7]Vatican [Cdim]Rag!