You mean Dany? And I don't know how she can offer more than her, the Lannisters have a huge debt with the Iron Bank, her forces are weaker than Dany's, she's completely untrustworthy after she decided to kill innocent people, which is exactly what the Mad King was about to do and she dares to use the argument of "But she's the daughter of the Mad King!!".
I guess I'll wait for the episode to see how she manages to persuade them and I hope they make it believable.
Edit: Btw, I'm not denying that Cersei can manage to use valid arguments like how Dany has an army of slaves and the Dothraki. Nevertheless, I'm talking about how can they end up trusting Cersei over Dany. In this case, actions speak louder than words, Dany has never killed innocent people while conquering cities and she has freed slaves, while Cersei has done a list of horrible things and almost everyone knows about them.
If I remember correctly, Dany actually has a somewhat good reputation, if she didn't, then Varys would've never risked taking Tyrion to her. So yeah, I can't see how Cersei will convince them unless she uses her power to intimidate them.