How did Renly expect Robert to set aside Cersei and take Margaery as queen instead?

Question

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:

1. Execute Cersei and be done with it.
2. 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?

Answer 1

Renly might have just been expecting Robert to act irrationally if Margaery looked enough like Lyanna.

• Robert's love for Lyanna was prfound (maybe even borderline obsession) as we know her "kidnapping" was one of the main reason for the start of his rebellion.

  Ned had loved her with all his heart. Robert had loved her even more. She was to have been his bride.

  "She was more beautiful than that," the king said after a silence. His eyes lingered on Lyanna's face, as if he could will her back to life. Finally he rose, made awkward by his weight. "Ah, damn it, Ned, did you have to bury her in a place like this?" His voice was hoarse with remembered grief. "She deserved more than darkness …"

  ...

  The king touched her cheek, his fingers brushing across the rough stone as gently as if it were living flesh. "I vowed to kill Rhaegar for what he did to her."

  A Game of Thrones - Eddard I

• Even Cersei was worried she would be replaced:

  My husband grows more restless every day. Having Stark beside him will only make him worse. He's still in love with the sister, the insipid little dead sixteen-year-old. How long till he decides to put me aside for some new Lyanna?"

  A Game of Thrones - Bran II

• Cersei also constantly tried to undermine Robert sometime's even in public:

  The mirth curdled on Robert's face. "The woman tried to forbid me to fight in the melee. She's sulking in the castle now, damn her. Your sister would never have shamed me like that."

  A Game of Thrones - Eddard VII

• Robert did not really want even marry Cersei in the first place:

  I had no wish to marry after Lyanna was taken from me, but Jon said the realm needed an heir. Cersei Lannister would be a good match, he told me, she would bind Lord Tywin to me should Viserys Targaryen ever try to win back his father's throne," The king shook his head. "I loved that old man, I swear it, but now I think he was a bigger fool than Moon Boy. Oh, Cersei is lovely to look at, truly, but cold … the way she guards her cunt, you'd think she had all the gold of Casterly Rock between her legs.

  A Game of Thrones - Eddard VII

• Robert's heartache runs deep:

  "Rhaegar … Rhaegar won, damn him. I killed him, Ned, I drove the spike right through that black armor into his black heart, and he died at my feet. They made up songs about it. Yet somehow he still won. He has Lyanna now, and I have her." The king drained his cup.

  A Game of Thrones - Eddard X

• Robert even committed one the worst faux pas between the sheets:

  Her eyes burned, green fire in the dusk, like the lioness that was her sigil. "The night of our wedding feast, the first time we shared a bed, he called me by your sister's name. He was on top of me, in me, stinking of wine, and he whispered Lyanna."

  A Game of Thrones - Eddard XII

---

Judging Robert's passion, fury, and fondness of drinking, Renly may have been right that he could convince Robert that Margaery was the perfect new bride because she looked like Lyanna. The fact that Tyrells may be the only power to challenge the Lannisters was just icing on the cake...

Answer 2

You're right that the premise as you've stated it makes no sense, because you're missing a key part - Renly knew about the incest.

This instantly makes his motivations sensible. He tells Robert that Cersei's children are not actually his, Cersei and the children are executed, and that leaves Robert as a middle aged king with no heir. He needs to marry again and have a son, so Renly introduces him to Margaery, who'd be a very reasonable choice anyway. This ends up with the Renly and his allies the Tyrell's as the new powers behind the throne, with the Lannisters massively out of favour.

That is the only way the plan makes sense - if Renly just wanted Robert to replace Cersei with Margaery, it wouldn't help the Tyrell's because the Joffrey would still be the next king - their power would die when Robert did, and Margaery would essentially have been wasted as a marriage prospect.

Olenna: "The thought that one day he may see his grandson with his arse on the Iron Throne makes Mace puff up like ... a puff fish" - ASOS Sansa I

Mace Tyrell wants his grandson as king, and he achieves that only if Cersei's children are out of the way.

The next question is how Renly found out, but this isn't really hard to imagine - Littlefinger, Varys, Jon & Stannis, and Ned all came to this conclusion, and Renly knew a lot of people at court, almost certainly had spies and would have been on the lookout for anything like this he could use to disadvantage the Lannisters. Renly also knows Edric Storm well, one of Roberts's bastards who perfectly demonstrates that Robert's actual children look like him.

Renly didn't reveal the incest as soon as he knew because his worst fear was that Stannis would end up as King - he needed to time it right so Robert could marry Margaery as soon as he was told, so there wouldn't be any risk of Robert dying and the crown going to Stannis.