Apparently the tune is from the traditional song "Boston Burglar" but I only know the Leslie Fish version.

BANNED FROM BEAUMONDE

Our crew were in high spirits from a mostly painless job

And Jayne was extra chipper thanks to post from Mrs Cobb.

They each set out to celebrate in their individual styles

And left a trail of stories that were talked about for miles.

Chorus: And they're banned from Beaumonde, everyone.

Banned from Beaumonde, just for having a little fun.

They went to walk the world a spell, for just three nights or four,

But Beaumonde doesn't want them any more.

The Captain bumped into a girl he’d met two times before.

‘Bout both of those occasions he still felt a little sore.

He gave in when she made big eyes and told him all her woes,

That is until he woke to find she’d stolen all his clothes.

Chorus: And they're banned from Beaumonde, everyone.

Banned from Beaumonde, just for having a little fun.

They went to walk the world a spell, for just three nights or four,

But Beaumonde doesn't want them any more.

Inara found a client with the coin for her large fee.

She’d make enough in one night’s work to fund a spending spree.

She kept her poise when in their joys came a loud and angry yell.

With a sultry look she calmed his wife and serviced her as well.

Chorus: And they're banned from Beaumonde, everyone.

Banned from Beaumonde, just for having a little fun.

They went to walk the world a spell, for just three nights or four,

But Beaumonde doesn't want them any more.

When the Doctor finally asked her out, l'ill Kaylee squealed in glee.

But for Simon dates with women didn't run so easily.

It wasn't long before once more he'd put his foot right in.

She dumped him for a fella with a much bigger engine.

Chorus: And they're banned from Beaumonde, everyone.

Banned from Beaumonde, just for having a little fun.

They went to walk the world a spell, for just three nights or four,

But Beaumonde doesn't want them any more.

Wash wanted to present his wife with a kind and thoughtful gift,

And so he bought for her to wear, a simple slinky shift.

It was a hit with all the men but one guy got too keen.

What Zoe did to that poor man is simply too obscene.

Chorus: And they're banned from Beaumonde, everyone.

Banned from Beaumonde, just for having a little fun.

They went to walk the world a spell, for just three nights or four,

But Beaumonde doesn't want them any more.

Now Shepherd Book’s a peaceful man, his private life is quiet.

They arrested him on Sunday morn’ for inciting whores to riot.

He was rescued from the chaos, mussed but none the worse for wear,

Except they stole his scrunchie, freeing all his fearful hair.

Chorus: And they're banned from Beaumonde, everyone.

Banned from Beaumonde, just for having a little fun.

They went to walk the world a spell, for just three nights or four,

But Beaumonde doesn't want them any more.

Now Jayne was not best pleased to find the whores had gone on strike.

He’d been planning a wild a party as you’ve never seen the like.

Despite his search he couldn’t find a girl to dine and bed,

But caused some frowns about the town taking Vera out instead.

Chorus: And they're banned from Beaumonde, everyone.

Banned from Beaumonde, just for having a little fun.

They went to walk the world a spell, for just three nights or four,

But Beaumonde doesn't want them any more.

Well River had been left behind to avoid those hands of blue.

But she got bored alone on board. Some fun was overdue.

She popped into a saloon to stock up on oaty snacks,

What happened next is anyone’s guess ‘cos none dare tell the facts.

Chorus: And they're banned from Beaumonde, everyone.

Banned from Beaumonde, just for having a little fun.

They went to walk the world a spell, for just three nights or four,

But Beaumonde doesn't want them any more.

Serenity’s a noble ship, the finest in the black,

But when her crew has downed some brew you’d better mind your back.

They leave a lot of wreckage, a few riots, some mayhem;

At least they’re sure that planet won't be quick forgetting them!