Either write your own, or adapt already made songs for ATLA here. I'll be posting My Swinging on a Star and DTVN's Rocky Horror here soon.

MoA's Original Post:

Leeeet's dooooo the tiiiiiime warp agaaaaain!

Zuko: Uncle! It's step-step, hip, step, twist, pout!
Sokka: I love the way these tights feel on me.
Toph: I can't see you, but I can tell you look ridiculous.
Aang: I would kill to be a wedgiebender.

DTVN's post:

Zuko: Help me, Mommy
I'll be good, you'll see
Take this dream away
What this, let's see
I feel sexy

Iroh: Ach! We've got to get out of this trap
Before this decadence saps our wills
I've got to be strong and try to hang on
Or else my mind, may well snap

Avatar Hawk: The Buddy Musical

*Aang and Zuko stand at the doorway to the Fire Nation capitol.*
Aang: Would you like to swing on a star?
Zuko: Carry Moonbeams home in a jar?
*Aang earthbends two columns to cause the portcullius to raise*
Aang: And be better off than you are?
*Zuko draws his swords*
Zuko: Or would you like to be a mule?
*Aang and Zuko move in, approaching a troop of Fire Nation soldiers, who ignite thier fists. Zuko looks to Aang, then points his open arms towards the soldiers in a "Go ahead" gesture. Aang wades into the army, slapping soldiers with his staff.*
Aang: A mule is an animal with long funny ears.
He kicks up at anything he hears.
His back is brawny
And his brain is weak
He's just plain stupid with a stubborn streak.
*Finished clearing the soldiers, Aang looks to Zuko who is confidently leaning against the wall, his arms crossed.*
Zuko: By the way, if you hate to go to school
You may grow up to be a mule.
*Aang and Zuko skip into the palace's main room.*
*Zuko points to Aang and flashes a thumbs up.
Zuko: Or would you like to swing on a star?
Aang: Carry moonbeams home in a jar.
Zuko: And be better off than you are?
Aang: Or would you rather be a fish?
*Zuko begins to scale the wall of the room, reaching a secret vent. He drops a rope to Aang*
Zuko: A fish is an animal that swims in a brook
He can't write his name or read a book.
To fool the people is his only thought,
And though he's slipperly
He still gets caught!
*Zuko kicks open the grate at the end and they emerge into the royal wing. Zuko winks at Aang, but Aang doesn't seem to be impressed.*
Aang: If that sort of life is what you wish
You may grow up to be a fish.
*Aang and Zuko march into the royal quarters and find the Firelord.*
Aang: Or would you like to swing on a star?
Zuko: Carry moonbeams home in a jar.
Aang: And be better off than you are?
Zuko: Or would you rather be a pig?
Ozai: A pig is an animal with dirt on his face,
His shoes are a terrible disgrace.
He's got no manners when he eats his food,
He's fat and lazy and extremely rude..
But if you don't care a feather or a fig
You may grow up to be a pig.
*Aang and Zuko get set into action and rush in. Aang airbends and pushes Ozai back into Zuko's attack range*
Aang: And all the monkeys aren't in the zoo
*Zuko swings his swords, but Ozai uses firebending to rocket in the air away from him*
Zuko: Every day you see quite a few
*Ozai throws out wave after wave of fire. Zuko encases Aang and himself in an orb of fire to protect themselves.*
Aang: So you see it's all up to you
Zuko: You could be better than you are!
*Zuko and Aang send out thier own fire blast, turning the Firelord to ashes.*
Zuko: You could be swinging on a star.
*He brushes the ash off of himself*
Aang: You could be swinging on a star.
*Aang brushes the ash off of himself*
Zuko: You could be swinging on a star.
*Zuko brushes the ash off of Aang*
Aang: You could be swinging on a star!
*Aang points at Zuko's shoulder, as if to signal that he missed some. Zuko checks and Aang hits his nose.*
Zuko: You could be swinging on a star!
*Zuko and Aang move thier heads closer*

And quick cut to something straighter.

Rocky horror forever!

The firelord would have to be Dr. Frankenfurter, and Aang would have to be Rocky!

And Sokka would be Bullwinkle!

(Never watched RHPS)