It sounds like your two players are having fun with this rivalry of theirs. It sounds like they aren't trying to be unreasonable. Given those circumstances, I wouldn't suggest that you try to defuse their rivalry in-game at all. On the contrary, why not see if you can bring the other players into it somehow and make it, at least temporarily, the focus of the game? Talk to everyone to make sure they're on board with the idea - and if the other players aren't really digging it, then maybe that will also drive home the point to the two rivals that they should tone things down for the sake of the rest of the group. But if everyone thinks it sounds cool, this could be one of the highlights of your campaign.
The trick is to involve the other PCs. They need to have some stake in the rivalry - maybe they want one side or the other to win, maybe they want everyone to get along, maybe they have some clever way to benefit from the situation no matter who wins, but they have to care for some reason. (And in fact, if everybody just wants everyone to get along, then that's a good sign that this isn't a great approach after all. You want this to be complicated and messy! And you want the players to care, not just the PCs.)
Let's say we have 5 PCs: Arthur, Bethany, Xavier, Yvette, and Zach. Arthur and Bethany want to kill each other.
I'd start by framing scenes between one of Arthur and Bethany (but not both!) and some of the other PCs, just to see what they have to say to each other. Maybe Xavier, Yvette and Zach already have some stake in the rivalry, or maybe they'll form an opinion during the course of talking about it.
Alongside this, take whatever else is going on in the PCs' lives, whatever it is they care about or whoever it is they have relationships with or whatever, and tie it up to the rivalry. See if you can find or create a reason why Zach's ambitions are served if Arthur dies, why Yvette's NPC friend is caught in the middle, why both Arthur and Bethany might really want Xavier to owe them a favor. Tie it to the rest of the setting, too: What organization does Arthur have rank in that might be angry if he's killed, or conversely, that might fall apart without him? What ally of Bethany's might want to get involved, with or without Bethany's approval? (What ally of Bethany's might notice that Yvette keeps hanging out with Arthur, and therefore conclude that Yvette needs to be taken out of the picture?)
Make everything a precarious balance and your two rivals the lynchpins. If Arthur or Bethany dies, everything will topple one way or the other, and the rest of the PCs stand to either be crushed by the falling rubble or else to climb up the pile of scree and stand victoriously at the top. Once you have that, all you have to do is sit back, play honestly, and see what happens!