Secrets & Lies (S&L) is a player-facing game, which means that every roll is based on the PCs' stats. This makes player-vs-player conflicts a little weird. S&L compounds the problem by making success the default state and using the dice to determine levels of failure. Put them together, and there's no convenient way for two PCs to compare rolls.
Truth be told, PvP conflict just never comes up in my sessions. Players always seem to work through their differences without resorting to mechanics, or they come at each other sideways (e.g. by deviating from the plan or sabotaging each other's relationships). Still, it's a legitimate point and there are ways to approach the problem. I'm going to work through a few of them here.
Victim Rolls
This method treats the instigating player, the one who wouldn't just walk away from the conflict, as an NPC. The "defender" rolls to resist whatever the "attacker" is trying to do: intimidate them, shoot them, steal from them, etc. The Director should take into account things like the attacker's Means and Motive when determining the size of the flop, but otherwise everything depends on the victim.
The Director names a relevant vital and the player boils it, using any relationships or secrets as appropriate. If they fail, the attacker gets their way. If they succeed, the attacker is thwarted. This does not entitle the defender to any retribution, they just don't get pwned. Any further escalation would allow the instigator to roll.
As with all PvP smack-downs, this could get tedious if players persist with the tit for tat reprisals. However, this method also gives defenders a clear advantage, which should discourage escalation.
Betrayer Rolls
If treachery is what you're after, you might want to approach PvP from the other direction. He who hits first gets to make the roll, leveraging relationships and secrets as appropriate, but the victim can increase the size of the flop by taking hits to relevant vitals on a 1:1 basis. I'd cap the flop at 5-6 dice, but that's just a suggestion.
This method gives betrayers a clear advantage, which means that first strike is a winner's strategy. If you're running a paranoid spy thriller, that might be just the ticket.
There's no reason you couldn't use this trick with the previous method, it's just that I was trying to _discourage_ treachery back then. In fact, if you wanted to even things up some more, you could let players buy flop dice by taking hits to relationships and secrets, too.
Trust Mechanics
I wanted to include some interesting trust mechanics with S&L, but nothing come together in my brain at the time. Now that I'm thinking about letting players influence the Flop... well, I've got a couple of ideas.
a) Trust as Reward - Between scenes, players can reward each other with Trust tokens (maybe just one at a time). Each token entitles the awarded player to immediately clear 1 hit from a vital of their choice. The only real incentive to reward another player is in the hope that they'll reciprocate, but that may be enough.
Trust tokens sit in a pile between the giver and the receiver. (This might get messy with a large group. Better write them down on note cards, just like everything else.) When one chooses to betray the other, the Trust tokens become flop dice on the victim's roll to resist. More trust = more pwnage.
b) Trust as Relationship - Again, each pair of players shares a "Trust" card. Both players can move dice out of their hand and onto this card any time one is helping the other. This method gives both players a clear incentive to put dice on the relationship. As above, when one betrays the other, the Trust dice become the victim's flop to resist.
c) Mistrust - As "a," but each pair of players starts with a Trust card full of hits. They can reward each other by removing hits between scenes, where every removal entitles the trusted player to clear 1 hit from a vital of their choice. During a betrayal, the remaining Mistrust hits become the _betrayer's_ flop. Less mistrust = easier betrayal.
At this point, I can't say for sure that any of these are what you'd call "good" ideas, but there you are. Comments and playtesting would be warmly welcomed.
--Dan