Unpopular Opinion: It was Snow.
I think it's clear, that Coin had motive and opportunity. Which is exactly why she couldn't have done it! I mean if she did, she certainly didn't do it all by herself (as explained above). And the point is that much like it would've come out if Snow were behind it, just the same goes the other way. Certainly, Katniss wasn't the only one who lost someone in the bombing. It would've come out. Someone would've put 1 and 2 together and come forward, tho she's clever, she's not the only one who can think...
Also, as mentioned by Snow himself, the war was over, they would've won one way or another imo Coin wouldn't have risked it.
So why Snow? Well, as said the he had already lost, BUT we know that the capitol has a gigantic (nuclear) weapon arsenal, probably wrong enough to blow everything to pieces. Which he probably would've done in such a situation. However, his main enemy in the entire movie is Coin. He want's to kill her more than Katniss or anyone else. Maybe, he even saw the bad in Coin in the end and wanted to prevent a second Panem. Therefore, instead of killing everyone he orders this horrendous, last strike to create the ultimate lie that convinces Katniss to kill Coin. Indeed, Snow is not wasteful. He uses Prim's death to 'kill' Coin.
Also, as @bluejayke mentioned Snow kept the gates shut, tho there's no real reason to.
To be fair, I haven't read the books, but assuming from this question and other answers it's never clearly stated who did it. So it makes sense to assume that something different happened.