Dunno if you've had these suggested:
BILL THE CAT

We had a cat: His name was Bill
He caught our budgie on the window-sill
One holy day; One Sunday morn
Left only feathers on our back lawn

Oh, no, Bill! You can't do that
You silly pussy; You stupid cat
So we took him down: Our family pet
And we left his balls, with the family vet

[strumming and cat yowling sounds in background]

Well the very next day, he packed his bags
Left all his Penthouse and Playboy mags
How could we do it; To the family pet
Go and leave his balls with the family vet

[spoken] Well we get no postcards; No telephone calls
         He's out in the bush somewher - with no balls
         And he's obsessed, with sweet revenge
         So eats our parrots. And our fairy wrens.

[chorus] Yes He's mortified and we all regret
         That we left his balls with the family vet [repeat]

[change of key]

Now he's highly sought, by the feral choir
For his new-found talent, to sing much higher
Has no more time; For female friends
Just for parrots - and Fairy Wrens

[spoken] No sense of humour. Ex-family pet
         It still hurts: He can't forget
         He's still angry: He's still upset
         That we left his balls with the family vet

[chorus to finish]

OR

CROCODILE ROLL

Hav'n a barbie by the river - with no-one else around
A tropical honeymoon; Knockin a four-ex down
She was standin in the water, eatin a pumpkin scone
when (chomp) - - - she was gone!

And they were doin' the Crocodile Roll: The woman and the reptile
Doin' the Crocodile Roll; In the middle of the river

Down came her husband. with a gun and a carving knife
To slaughter every crocodile for takin 'is darling wife
[spoken with a pronounced stutter - in whiney old man's voice]

Y-you c-c-can't g-g-g-go round eatin' Q-Q-Q-Queenslanders you overgrown g-g-g-goannas; I'll turn you all into sh-shoes (CHOMP) oooh!

And they were doin' the Crocodile Roll: The husband and the reptile
Doin' the Crocodile Roll; In the middle of the river

Down came his bloodhound; with mangy, curly hair
Picked up the scent; away he went; bum in the air
Then the dog got carried away and ran out on a log
An' (CHOMP) Guess what! No more dog!

And they were doin' the Crocodile Roll: The canine and the reptile
Doin' the Crocodile Roll; In the middle of the river

Down come a wild pig: rootin' all around
The little swine drank some wine and really pigged it out
Then the crocodile chased him 'round
An' the little pig yelled "Up Yours!"
(CHOMP) Into another croc's jaws!

And they were doin' the Crocodile Roll: The porker and the reptile
Doin' the Crocodile Roll; In the middle of the river

There's no moral to the story; just a brand-new dance
Grab your partner by the neck and swing your crocodile pants
Dip your toe in the water, are you ready for romance?
Swirl your tail around the floor; c'mon take a chance!
Now you'rE doin' the crocodile roll; stirrin' up the mud
Doin' the crocodile roll in the middle of the river
They were doin' the Crocodile Roll: stirrin' up the mud crabs
Doin' the Crocodile Roll; In the middle of the river.


OR

THE BUDGIE SONG

Well it cost me thirty bucks to fix me Budgie
When the little blighter only cost me five
The veterinary surgeon saw me coming
But I had to keep my 'feathered friend' alive

He was shakin' on his perch; the kids were crying
The family gathered 'round hi little cage
I said "I think it's time we got a new one"
That's when the family went into a rage!

Oh the waiting-room ponged like a rat-house
With heart-worm and lung-worm and lice
And a Persian had its eye on the shoe-box
I suppose she thought our Budgie might be nice.

Well the bird shit on the veterinary surgeon
I heard him say "the dirty little chick"
Guess he wondered why I didn't use m' brains
And hit him over the head with a brick

[chorus]Oh! Antibiotics for his colour
       Three drops a day on his beak
       Some powder on the nose for his feathers
       And clean out his cage twice a week

Well it cost me thirty bucks to fix me Budgie
When the little blighter only cost me five
And the bludger wakes me early in the morning
It's got me puzzled how he survives

One night I'll feed him to the tom cat
Instead of worrying about him when we go away
No-one wants to feed a shitty Budgie
When everyone's on holiday

[finish with the chorus - twice]

You can clean it up by singing 'pooped' instead of shit in V4
and skungey (pronounced 'skun-gee') instead of 'shitty' in V6

OR
OLD MAN EMU

Let me tell you bout an interview with an old man emu
He's got a beak and feathers and things
But the poor old feller ain't got no wings
Aren't you jealous of the wedge-tailed eagle
'oom-ba-da-little-la-dah-dah
While the eagle's flyin' round an' round; I keep me two feet firmly on the ground
Now I can't fly, but I'm tellin' you -
I can run the pants off a kangaroo!

Ba da doo doo da doo doo doo: Doo da doot doot doo doo
He can't fly but i'm tellin you -
he can run the pants off a kangaroo.

Well he was the model for the fifty cents
Oom ba da ... (etc)
The designer should've had more sense
Oom ba da ... (etc)
If ya take a look it'll prove to you ...
I ran the pants of the kangaroo
Ba da doo doo da ... (etc)

Ya can't loop-theloop like a cockatoo
oom ba da little la dah dah
Swoop an toss like an albatross
oom ba da ...(etc)

[spoken]
Ya silly galah, I'm better by far
Than a white cockatoo or a budgerigah (pron: Budge-er-ee-gar)
They squeak an squawk an try t' talk
Why me an them's like cheese an' chalk

Ba da doo ...(etc)

Dingo came around one day
oom ba da ...(etc)
Hey there, emu; Ya wanna play?
Oom ba da ... (etc)
But the emu was too smart for him
walked right up an' kicked him in the shins

Ba da doo doot ...(etc)

Well the last time I saw old man emu
oom ba da ...(etc)
He was chasing a female he knew
oom ba da ...(etc)
As he shot past I heard him say
[very heavy panting followed by narration in TOTALLY puffed out voice]
She can't fly but I'm tellin' you ......
She can run the pants off a kangaroo!

Well there is a moral to this ditty
oom ba da ... (etc)
Thrush can sing, but he ain't pretty
Oom ba da ... (etc)
Duck can swim, but he can't sing, nor can the eagle on the wing
Emu can't fly but I'm tellin' you
He can run the pants off a kangaroo
Well the kookaburra laughed and he said "it's true"
Oom ba da ... (etc)
Ha ha ha ha hoo hoo hoo! He can run the pants off a kangaroo.

OR (a sensitive one)
GOODBYE BLINKY BILL

Oh goodbye Bunyip Bluegum; Goodbye Blikky Bill
And beautiful little Nutsie; I can't believe it
Our koalas are all dying can it really be?
A national disaster; a world catastrophe

Shiny little black nose and fluffy little ears
Furry little bundle, soaking up the tears
Oh Snugglepot and Cuddlepie are crying in the rain
And Wombat's gone into his hole and won't come out . . . .

[chorus]
Oh pass the hat around between your friends
There's no time to contemplate
Maybe if we show some love; maybe it's not too late

'Cause Blinky Bill is dying: Cross him off the list
Knock on doors, ring the bell, save the Eucalypt
I don't think I could stand the shame, knowing that I could ...
Have saved the world from losing something beautiful and good

[chorus]

One doctor on the job is hardly enough
One little hospital: Wake up, Australia!
It's our corner of the world; time to pull our weight
What would we tell our children about our little mate?

[Repeat verse one]

[finish with chorus]

NOTE:

Blinky Bill, Nutsie and Wombat are all characters in favourite traditional children's story books "The Complete Adventures of Blinky Bill" by Dorothy Wall; while Snugglepot and Cuddlepie are "Gumnut Babies" - the creation of English-born writer May Gibbs who, after settling in Australia, decided we needed our own 'indigenous' fairy stories and traditions. And so "The Complete Adventures of Snugglepot and Cuddlepie" was born

These songs are all the creation of Australian songwriter and singer John Williamson. His 25th Anniversary CD of "True Blue" should have all five songs and I can supply chords as I play them as well.

I can also answer any questions on colloquialisms and Australianisms you might find 'odd'.

Muttley

There are also

"Somebody's Moggy" by Eric Bogle - sung in a barber-shop quartet-like mode or "Nobody's Moggy" sung to the tune of "No Man's Land - the Green Fields of France". I can supply the words to both of these as well if you wish