We know that Renly wanted Robert to set aside Cersei and take Margaery Tyrell as his Queen instead.
He had this weird idea that Margaery looked like Lyanna and Robert who was still in love with Lyanna would be expected to like her.
A few days past, he had taken Ned aside to show him an exquisite rose gold locklet. Inside was a miniature painted in the vivid Myrish style, of a lovely young girl with doe's eyes and a cascade of soft brown hair. Renly had seemed anxious to know if the girl reminded him of anyone, and when Ned had no answer but a shrug, he had seemed disappointed. The maid was Loras Tyrell's sister Margaery, he'd confessed, but there were those who said she looked like Lyanna. "No," Ned had told him, bemused.
AGOT - Eddard VI
Then Robert told Eddard that Renly had talked to him about Margaery and her beauty.
Have you seen Mace Tyrell's boy? The Knight of Flowers, they call him. Now there's a son any man would be proud to own to. Last tourney, he dumped the Kingslayer on his golden rump, you ought to have seen the look on Cersei's face. I laughed till my sides hurt. Renly says he has this sister, a maid of fourteen, lovely as a dawn …"
AGOT - Eddard VII
Varys also knew about it:
The Knight of Flowers writes Highgarden, urging his lord father to send his sister to court. The girl is a maid of fourteen, sweet and beautiful and tractable, and Lord Renly and Ser Loras intend that Robert should bed her, wed her, and make a new queen.
AGOT - Arya III
Then Stannis openly said it out loud:
"We both know your wedding was a mummer's farce. A year ago you were scheming to make the girl one of Robert's whores."
"A year ago I was scheming to make the girl Robert's queen," Renly said, "but what does it matter? The boar got Robert and I got Margaery. You'll be pleased to know she came to me a maid."
"In your bed she's like to die that way."
ACOK- Catelyn III
Now with the core premise established, the question is, how did Renly expect that to work out?
Robert was already married to Cersei and they were both followers of the Seven. In the Faith, a marriage which has been consummated can't be annulled and there is to be no polygamy (unless you have dragons). How did Renly expect Robert to set aside Cersei?
I can only think of two ways he could have done it:
- Execute Cersei and be done with it.
- Pack her off to the Silent Sisters like Ser Quentyn Ball did in order to secure entry into order of the King's Guard.
Neither of those two solutions seem to be do-able. Cersei's father, Lord Tywin was basically Robert's wallet, sending her to Silent Sisters would put an end to that unfathomable pocket (Although it would have secured Lord Tyrell as the new Crown-purse) and be a slight on honor of Casterly Rock and Lord Tywin wasn't a man to forgive such things. Executing her would incur Lord Tywin's wrath, power of the Casterly Rock was just as impressive as her wealth, if not more. So how exactly did Renly think that could possibly happen?