Charisma, if I remember my AD&D correctly, had basically two parts - personality, and leadership ability.
As idols, personality is basically a given. So it boils down to leadership, the ability to persuade people to follow you.
The straightforward answer is Airi, for reasons mentioned in my favourite voice post. I'd follow her to the ends of the earth after listening to that performance of Aa Koi.
Another way to look at the question is from an idol context - how are they as leaders of idols?
Now that's trickier.
As far as leaders of idols in H!P are concerned - Aichan, Maimi, Momo, Dawa - plus one Captain, don't appeal to me as charismatic leaders per se. I don't know the past leaders of MoMusu, though I hear Yossie was a good one. Takamina's another one I've heard, but I'm not familiar with her in the context of being a leader.
Makes me wonder - in H!P concerts, is there one character that everyone will follow? Kamei was actually very good at catching everyone's attention, not necessarily by orthodox means. But that isn't exactly leading, is it?
So who does anyone follow in a H!P concert. One answer comes to mind - Makoto, everyone's favourite middle-aged MC with a mushroom haircut.
Yup, all the H!P idols definitely listen and follow his lead in concerts.
As a parting gift, here's the cover for Melon Kinenbi's 'Charisma Kirei'. Irrelevant but still on-topic
P.S. I also think there's a term 'Charisma Idol'. I wouldn't know what it would mean to be an uncharismatic idol, but I have heard that term being bandied around.