Circei does benefit more obviously than anyone else - Margaery was going to take her out of the picture as a powerful player. But it’s been shown over and over again that love for her children is a primary motivation for her, so I’m not sure I could buy it. Maybe if you consider how she gradually loses control of Joffrey as he becomes more and more of a monster throughout the series, but it’s hard to believe she’d kill her son.
It would also be logistically difficult. If we assume this poison is quick acting - which, in terms of storytelling, is a fair assumption - it would be somewhat unfair if it was on a 2 minute delay, and he just coincidentally started reacting to it when he started drinking again a while after ingesting the lethal dose, then the timeline goes like this:
Joffrey kicks the goblet under the table, Sansa grabs it and returns it to Tyrion, who offers it to Joffrey. Joffrey orders Tyrion to fill it. He takes the carafe of wine, which is placed in front of Cercei, and fills it, offering it to Joffrey. That’s when Joffrey orders him to kneel, and Margaery distracts him with the pie ceremony. At that point he takes the cup, takes a gulp, and hands it to Margaery, who puts it down on the other side of the central table, closest to Olenna.
At this point, if the poison is quick acting, then he’d start having symptoms right then, but he doesn’t. Which rules out Sansa doing something when she retrieved the cup, and the carafe of wine being poisoned before Tyrion pours it into the goblet.
Joffrey chops the ceremonial pie, some servants bring some real pie, and Margaery feeds some to Joffrey. His piece being poisoned specifically is a possibility, but the poison wouldn’t be acting right away if that were the case. There’s a good 50 seconds between him eating the pie and the symptoms starting.
He orders Tyrion to serve him his wine - Tyrion walks over, picks up the cup, and the camera shows Olenna in the frame with the cup, looking at Tyrion. He hands Joffrey the cup, he drinks, and the symptoms begin within 5 seconds.
So if the poison is fast acting, it came from the wine, which must have been tampered with at some point after Margaery takes it from him to set down. Circei isn’t close enough to have access to it at that point. Only Margaery or Olenna plausibly could reach it. Or it’s not fast acting, and he could’ve been poisoned at any time in the last few minutes, in which case it’s really hard to say, but that’d be a bit of cheat in storytelling terms, I think.