Can't help you with your question, Leeneia, but this is an interesting song to explore.

This PDF has chords for both versions, which may help you adapt the tune: http://www.kristinhall.org/songbook/OldChestnuts/Tessie.pdf.

There's a Wikipedia page on the song.

I also found a music box recording of the 1902 song:
https://www.youtube.com/watch?v=d8hfFuNaMWU

And a 1903 recording by Billy Murray:
https://www.youtube.com/watch?v=j-5FIUHlPYM

There is sheet music at the Library of Congress

And a very interesting Web page titled The Historic Tale of Michael "Nuf Ced" McGreevey, the Royal Rooters, "Tessie", and Red Sox Nation

And here are the Dropkick Murphys lyrics:

TESSIE
(Dropkick Murphys Version, 2004)

Tessie is the Royal Rooters rally cry
Tessie is the tune they always sung
Tessie echoed April through October nights
After serenading Stahl, Dinneen and Young
Tessie is a maiden with a sparkling eye
Tessie is a maiden with a love
She doesn't know the meaning of her sight
She's got a comment full of love

And sometimes when the game is on the line
Tessie always carried them away
Up the road from "Third Base" to Huntington
The boys will always sing and sway

Two! Three! Four!

Tessie, "Nuf Ced" McGreevey shouted
We're not here to mess around
Boston, you know we love you madly
Hear the crowd roar to your sound
Don't blame us if we ever doubt you
You know we couldn't live without you
Tessie, you are the only only only

The Rooters showed up at the grounds one day
They found their seats had all been sold
McGreevey led the charge into the park
Stormed the gates and put the game on hold
The Rooters gave the other team a dreadful fright
Boston's tenth man could not be wrong
Up from "Third Base" to Huntington
They'd sing another victory song

Two! Three! Four!

Tessie, "Nuf Ced" McGreevey shouted
We're not here to mess around
Boston, you know we love you madly
Hear the crowd roar to your sound
Don't blame us if we ever doubt you
You know we couldn't live without you
Tessie, you are the only only only

The Rooters gave the other team a dreadful fright
Boston's tenth man could not be wrong
Up from "Third Base" to Huntington
They'd sing another victory song

Two! Three! Four!

Tessie, "Nuf Ced" McGreevey shouted
We're not here to mess around
Boston, you know we love you madly
Hear the crowd roar to your sound
Don't blame us if we ever doubt you
You know we couldn't live without you
Tessie, you are the only only only
Don't blame us if we ever doubt you
You know we couldn't live without you
Boston, you are the only only only
Don't blame us if we ever doubt you
You know we couldn't live without you
Red Sox, you are the only only only