So, you want to balance stunt utility...
If you look at most of the example stunts, you'll notice that the circumstances under which you can use them are pretty narrow compared to the base skills they modify. That's the sweet spot you want to shoot for with your own stunts - you want them to be limited enough in scope that it feels special when you use them, but not so narrow that you never see them come up after you take them.
If the stunt effectively takes over all of the skill's base actions, it's not limited enough. You don't want a stunt replacing the skill it modifies.
The two main ways to limit a stunt are by keeping its effects to a specific action or pair of actions (only creating an advantage or only attack and defend rolls), or by limiting the situations in which you can use it (only when you're among nobles, only when it deals with the supernatural, and so on).
For the best results, use both - have the stunt restricted to a specific action, which can only be used in a very specific in-game situation. If you're worried about the situation being too narrow, back up and think of the ways the skill might be used in play. If you can see the stunt being relevant to one of those uses, you're probably on the right track. If you can't, you may need to adjust the stunt a little to make sure it'll come up.
-- "Balancing Stunt Utility", from the Fate SRD
So, looking at a replacement stunt from the game's sample character sheets:
Friendly Liar. Can use Rapport instead of Deceive to create advantages predicated on a lie.
And that kind of seems like it just replaces all uses of Deceive to Create an Advantage? But Deceive's Create an Advantage actions span combat feints, momentary distractions in for example contests, and longer cover identities. You might say that the Friendly Liar stunt is only limited to the last use of it, since saying "look over there!" isn't really a super-friendly thing?
The guidance applies both to replacement and to +2s, so if you wanted to come at this from another direction, you could say something like:
Why Can't We Be Friends? +2 to Rapport when you try to charm or persuade someone hostile to you.
And before you recoil back, all like "oh lord the player's already doing that and you want to make it easier?", I'd like to introduce you to an often-overlooked friend of mine called passive opposition.
Sometimes stuff's just hard.
When you shoot at somebody in pitch blackness, trying to hit them based on how well you can pin down their location without vision, how is that different from shooting at somebody in the middle of an open field?
Well, when you shoot at somebody in the middle of an open field, what makes it hard is how good they are at getting out of the way. When you shoot at somebody in pitch blackness, what makes it hard is that it's freakin' dark. The darkness is providing a passive opposition, and it doesn't matter if your target's rubbish at dodging, it's +7 Epic to be on target in pitch blackness.
You can treat hostility in a similar way. Rapport's function is kind of predicated on a positive or at least a neutral social atmosphere, right? It doesn't matter how susceptible somebody might be to a friendly smile on a regular day, they've been ordered to kill you and that puts up a passive opposition.