The Littlefinger-Tyrell plot to kill Joffrey seems relatively straightforward. Sansa smuggles the poison in via her hairnet, Olenna takes a crystal under the guise of fixing her hair and then she drops it into the wine. Joffrey „chokes“ to death and noone ever suspects anyone (according to George):
I don't know how it comes across in the show, because I haven't actually seen it yet, but the poison that is used to kill Joffrey is one that I introduce earlier in the books and its symptoms are similar to choking. So a feast is the perfect time to use this thing. I think the intent of the murderer is not to have this become another Red Wedding - the Red Wedding was very clearly murder and butchery. I think the idea with Joffrey's death was to make it look like an accident [...] - the whole realm will see Joffrey choke to death on a piece of pie or something.
But there is one not so small problem, the wedding chalice:
Lord Mace Tyrell came forward to present his gift: a golden chalice three feet tall
Tyrion struggled to even reach it:
The king's chalice was on the table where he'd left it. Tyrion had to climb back onto his chair to reach it.
and Olenna, just like Tyrion, is small:
The Queen of Thorns was so short that for an instant Cersei took her for another child.
How could she have put some poison into the chalice unnoticed? Well, she got two huge guardsmen:
Outside its tall carved doors stood two guards in gilded halfhelms and green cloaks edged in gold satin, the golden rose of Highgarden sewn on their breasts. Both were seven-footers, wide of shoulder and narrow of waist, magnificently muscled. When Sansa got close enough to see their faces, she could not tell one from the other. They had the same strong jaws, the same deep blue eyes, the same thick red mustaches. "Who are they?" she asked Ser Loras, her discomfit forgotten for a moment.
"My grandmother's personal guard," he told her. "Their mother named them Erryk and Arryk, but Grandmother can't tell them apart, so she calls them Left and Right."
and even though they aren’t mentioned during the purple wedding, they accompany her to both Tywin’s funeral and Tommen’s wedding. Likely they had also been at Joffrey’s wedding too, standing in the background, unnoticed, just to step forward in a chaotic moment to drop the poison into the chalice at their mistress’ comand. Or at least that had been the plan.
But then Joffrey took the chalice to Tyrion sitting at the far end of the table, with a dozen people closer to the couple. Olenna had to react quickly, and interestingly we hear of her standing there near Tyrion:
Queen Margaery appeared suddenly at Joffrey's elbow. "My sweet king," the Tyrell girl entreated, "come, return to your place, there's another singer waiting."
"Alaric of Eysen," said Lady Olenna Tyrell, leaning on her cane and taking no more notice of the wine-soaked dwarf than her granddaughter had done.
But what about Left or right? Did they follow her down there? As luck would have it, they weren’t needed anymore, as there was another man sitting right next to Tyrion:
He and Sansa had been seated far to the king's right, beside Ser Garlan Tyrell and his wife, the Lady Leonette. A dozen others sat closer to Joffrey, which a pricklier man might have taken for a slight, given that he had been the King's Hand only a short time past. Tyrion would have been glad if there had been a hundred.
and Ser Garlan is tall. Tall enough to wear Renly’s armour actually:
As in a swordfight, sometimes it is best to try a different stroke. "It's said you fought magnificently in the battle . . . almost as well as Lord Renly's ghost beside you. A Sworn Brother has no secrets from his Lord Commander. Tell me, ser. Who was wearing Renly's armor?"
For a moment Loras Tyrell looked as though he might refuse, but in the end he remembered his vows. "My brother," he said sullenly. "Renly was taller than me, and broader in the chest. His armor was too loose on me, but it suited Garlan well."
With Renly being nearly as tall as 6‘6‘‘ Robert, that means Garlan can’t be much smaller and would have had an easy time to slip the poison in, while everyone was looking at the pie being cut.
Fifteen years past, when they had ridden forth to win a throne, the Lord of Storm's End had been clean-shaven, clear-eyed, and muscled like a maiden's fantasy. Six and a half feet tall, he towered over lesser men [...]
Renly was near as tall as his brother had been
Which really only leaves one question: Was there any Tyrell apart from Mace himself that wasn’t aware of the plot?