Cersei wouldn't kill her own kid. To her, Joffrey is just a little unruly and stubborn. She doesn't see the monster that everybody else does. No way she'd kill her kid.
Tywin wanted to teach Joffrey a "sharp lesson". Can't learn a lesson when you're dead. To understand Tywin, you gotta realize Tywin's father was a BYTCH. A HERB. A LAME. The lords in the Westerlands were openly disrespecting his Lord father Tytos, not paying taxes. So a 15 year old Tywin had to take over and destroy the two houses that wanted beef. That's why he's so adamant about Lannister pride, Lannister dominance, leaving a strong legacy. He wouldn't kill Joffrey like that, having him choke on his own spit like a fool in front of all of Westeros, because it makes his family look bad. He wouldn't kill Joffrey period. If he was a kinslayer, Tyrion would have gotten killed YEARS AGO.
Littlefinger surely had something to do with it. I notice he wasn't around at the Wedding. He's always behind everything.
Varys surely had something to do with it as well. He has his hands in everything. He either conspired with Littlefinger or he atleast knows.
Oberyn is a red herring. He hates the Lannisters but, I don't think he'd kill a teenaged boy at the largest event in the country. Not his style really.
Lady Olenna. Alot of signs point to her. Margery is her favorite granddaughter. If you think she would let Margery get married to some crazy little psycho who would eventually start abusing her, then you're crazy. No way. In Westeros, its common for the younger brother to marry the widow. Remember when Brandon Stark got killed by the Mad King Aerys. Ned Stark stepped up and married Catelyn. So maybe The Tyrells were planning on getting Tommen from the jump. He's like 10 years old, Margery is supposed to be like 17 years old. Margery would essentially run the kingdom and even after Tommen grew up, he would have gotten molded to be loyal to the Tyrells. Whereas Joffrey is a fukkin psycho who wouldn't be controlled. I see your motive Lady Olenna, I see it
I could also see a scenario where Loras Tyrell became the second "Kingslayer", killing Joffrey years from now after Joffrey started abusing Margery, because you know he would. Maybe that factored into the Tyrell's decision.
Another thing about Littlefinger. Wasn't he the one to go make the Alliance with the Tyrells when Stannis was coming with those ships?
Maybe Littlefinger and Lady Olenna agreed on something else
Petyr Baelish - Game of Thrones Wiki
Renly is killed in mysterious circumstances and Littlefinger then approaches the Tyrells with a new proposal of alliance with Joffrey. This will allow Margaery Tyrell to remain a queen and provide Loras Tyrell vengeance on Stannis. He leaves the camp with them for Highgarden.
[17] Catelyn acts alone to free Jaime on returning to Robb's camp, just as Littlefinger suggested.
[18]
Littlefinger travels to
Harrenhal to propose an alliance between
House Lannister and
House Tyrell to Lord
Tywin Lannister.
[19] Littlefinger is successful in negotiating with the Tyrells and the allied forces arrive in time to claim victory at the
Battle of the Blackwater