I agree with Hp Shout that Katniss only agrees to the Hunger Games proposal to stay in Coin's good graces, but I don't think she did it (at that moment) in order to kill Coin.
I think Katniss is a terrible mess at this point in the book, barely hanging on to her sanity. The one thing that keeps her going - the thing she needs above everything else - is to kill Snow. In this state, she knows that no one is likely to trust her much, and certainly Coin has never trusted her. Katniss suspects that the HG proposal is a final loyalty test. Coin has explicitly said that she will only honor her promises if Katniss does everything Coin asks of her. Besides, if Coin allows Katniss to play this powerfully symbolic executioner role and then Katniss turns on Coin, it would be a disaster for Coin. So Katniss knows that if she wants to kill Snow (for Prim and everything else she blames on Snow), then she needs to support this HG proposal. No matter how wrong and it is. No matter how much it tears her up. She is still in the Games.
But when she faces Snow, I think the horror of what she had to do to get there is to much for her, and the decision to kill Coin is essentially involuntary. I don't think she rationally decided that Coin had ordered Prim's death. But suddenly the idea of Coin's guilt, which she had been trying to ignore and suppress, was all too easy to believe. And now she knew that Coin was evil, just as evil as Snow. In fact... Coin is the new Snow. And she is there to kill Snow...