Cersei could not have children.
She had fallen pregnant with Jaime's child back when they were only teenagers, before she was married. It would not do. So she braced herself, took the moon tea and nearly clawed her eyes out in sorrow as she bleed their baby out. She never told Jaime.
She did not know if it was that that caused her to be barren, but it seemed likely.

Now and again she'd swell as Robert's seed took, and she'd get a hopeful ten to twelve weeks or so, and then she'd lose them again, her children.
Cersei knew that she was only going to be Queen so long as they thought she could have children. If a Queen could provide no heirs, she was useless and she'd be replaced somehow. Cersei did not that think they'd kill her outright but they'd find some loop hole to let Robert marry some younger, capable lady.
She could not let that happen. She was Cersei Lannister, Lioness of Casterly Rock and she was the Queen.

Cersei knew on some deep instinctive level that Jaime could give her a child. He had before and he could do again it, but her brother was away at the Wall, and no use to her.
She often thought that this was the Gods way of showing her that her and Robert were not meant to be.

With no other options, she approached Littlefinger.

"I must say your Grace, I did not anticipate such a meeting. I am honoured," Littlefinger said, sounding utterly bored, as they sat in her chambers that night.
Cersei sipped her wine demurely before she spoke.
"Robert tells me you have quite a talent with money."
"Did he? I'm glad to hear it your Grace. I do try."
His gray blue eyes stared at her, silent inquiring as to the real reason why she had summoned him.
"Leave," Cersei commanded the various handmaidens that littered the room.
They scampered away and she waited until the door had closed behind them before she spoke again.

She stood and came over to Littlefinger's side, her golden hair sweeping around as she moved.
"Can I trust you, Lord Baelish?" she asked softly.
He waited a long moment before speaking.
"King's Landing is not a place where I would recommend trusting anyone, your Grace."

She went back to her seat, annoyed.
"I am the Queen. You are a little low-born man with no titles, no army, no leverage to speak of. If you betray me I will destroy you."
He looked at her, almost disdainfully, and then smiled.
"I would never dream to betray the Queen's trust."
Cersei reckoned for all his smiles, Littlefinger would never risk his own skin, and so she slowly explained to him what she needed.

After that, she had three children.
Robert had managed to make her quick again a few months after her and Littelfinger's chat, but this time she saw fit to actually inform the King. Normally she hid her half-pregancies, knowing she would only disappoint him when they failed.
She also told Littlefinger, who scoured the city's brothels for a pregnant whore, which wasn't too hard to find.
Cersei lost the child ten weeks in this time, but let nothing on. She had her handmaidens stuff the front of her robes, and refused to let Robert see her naked on the grounds that she was embarrassed by the way the pregnancy had ruined her body, and that she didn't want him seeing her like that.
Her husband was a useless oaf, and liked his ladies young and pretty, as so was glad to ignore her and her seemingly swollen belly.

Robert went off hunting as she neared the end of her pregnancy, and when he returned, she had a beautiful baby boy in her arms.
One whore left that day with a heavier purse, and told everyone she knew that her baby had died at birth. It was a simple arrangement, and so the king had his heir, and Cersei remained Queen.

Cersei's three children were beautiful. She named them after family, as if that somehow made them truly hers.
Edwin was her eldest, for Robert's beloved Eddard, and her own father Tywin.
He had dark hair and arresting brown eyes. That whore had served them well, so Cersei got two other children by her, who were both brown-eyed like their brother, but what did that matter?
Tyanna's name was mix of Cassana, who was Robert's late mother, and Joanna, her own mother, and Tyrion, her hideous younger brother. Tyanna was so beautiful Cersei often thought she must be hers truly. She wondered how some common whore had such perfect children.
Her youngest was called Jai for her twin, and she loved him the most.

Littlefinger came to her years later, when Edwin was twelve.
"Your Grace, you asked me to come to you if I ever heard that anyone was curious about our little arrangement."
She waited but he didn't elaborate. "Yes, yes, out with it then."
"Well, I have been told that the King's Hand, Jon Arryn, is asking why the King's three children have brown eyes when Robert has blue eyes and his wife green?"
Cersei stared at him blankly, and then understood.
"Will he find out?" she whispered.
Littlefinger titled his head. "That is difficult to say, your Grace, but the consequences would be most unfortunate."
That could not be allowed happen. Cersei wished Jaime were there. He would kill anyone who dared question her.
But her twin was at the Wall, and she did not know what to do next.