To start you off, here are a few I've written. Under the cut for dirtiness.
There were three young boys in a tower
Who found the most int'resting flower.
Kon-El took a sniff,
And Timmy got stiff,
So Bart did vibrate for an hour.
There was a young man called Bernard
Who learned that his friend Tim was scarred.
He touched them with care
And thought it unfair
That Robin could make him so hard.
There was a young Batgirl called Cass
Who could tell Spoiler's mood from her ass.
'In love' was Steph's mood,
So Batgirl she wooed,
And she cuddled with her in the grass.
ETA: Two more!
There once was an archer named Roy
who buried his shaft in a boy.
He pleasured his Dick
With a kiss and a lick.
'Til Dickie was shouting with joy.
There once was a speedster called Bart
Who felt a strange flutter at heart.
He found his Blue Bug
and gave him a hug,
Of something great that was the start.
There once was a fourth little bird
Who'd fallen in love with the third.
She found her boy Tim
And cuddled with him.
It wasn't till dawn that she stirred.
There once was a young Martian White
Who woke very close to midnight.
She had just been pounced
By a girl who could bounce
Who kissed her with all of her might.
There once was a clever red head
Who found a Canary in bed.
Her favorite bird
Did not speak a word,
Just kissed her and hugged her instead.
PC really did like his charts,
And Mac fell in love with the arts.
They bickered away
Until one fine day,
They found something else in their hearts.
There once was a mother who let
Her daughter become Arrowette.
She thought it was great,
Didn't see Cissie's hate,
For the costume, the blood, and the sweat.
M'gann didn't want to be bad,
And Rose really hated her dad.
M'gann did love Rose,
So she did propose,
And now neither one can be sad.
Ted had brains and courage galore,
But his heart pains he couldn't ignore.
His buddy said bull,
And that heart he stole.
"I'll let nothing harm it," he swore.
Timmy's work never was done
And he'd train till the rise of the sun.
Rose told him, "Relax."
And pulled off his slacks,
Then sucked him until he did come.
There once was a merc-with-a-mouth
Who decided to take a trip south.
He found his pal Cable,
And snuck under the table,
Then shouted, "Ha! This limerick doesn't end right! Or make any sense!"