What kind of check would it be if a player wanted to slap on binders to a target that is attacking him or a teammate?

Athletics/Coordination vs. Athletics +2 setback? or something different, or just plane no.

Unless they have done some kind of pinning or grappling maneuver I wouldn't even allow a check without it. Athletics or Coordination to do that would be fine, or some kind of Brawl check.

There's a great many choices and most of them work - if I were GMing, I'd probably go opposed Brawling check, but if it were Jackie Chan flipping and jumping and trying to grab the wrist of his opponent, I could see athletics. Hell, if you're Inspector Zenigata, I could see ranged light.

So really its all in the characters approach.

On more than one occasion people have asked about trying to apply a restraining bolt to a droid as, essentially, a melee attack in the middle of combat. The general consensus was that such a thing should be declared virtually impossible unless the droid in question was somehow firmly restrained.

Binders are less complex and easier to apply than a restraining bolt; but I would still make basically the same ruling. I would only allow someone to attempt to apply them if the target is restrained enough that he can't effectively move his limbs. I would never normally allow binders to be applied as a "melee attack".

Observe, for example, that police officers don't square off against criminals, weaving and feinting, before diving in for a perfectly timed "handcuff attack". They wrestle a criminal to the ground, hold him firmly (ideally with the combined strength of at least two officers), and then apply handcuffs while the target is incapable of significant resistance.

I like the cinematic style of that kind of attack. I might make it an opposed Brawl roll, where the difficulty is set by the opponent's skill. Likely to get some red dice in there, and hopefully discourage it as a go-to move.

A despair would also result in the combatants being cuffed together. That would encourage some interesting moves in subsequent rounds.

Rules say that grappling is generally just Brawling when trying to do Strain damage. So I'd probably have it Brawl opposed by the target's choice of Athletics, Coordination, and Brawl.

personally I would treat it as a brawl or melee attack keyed off the primary weapon with a setback to two toggled on depending on cercumstance. With any triumphs or 2 advantages rolled allows you to cuff one hand, 3 to cuff both in addition to any damage dealt. To reflect that in trying to restrain the subject they are really beating into them to gain the upper hand, but even if they win the round hey might not necessarily cuff them. A defeated opponent is automatically cuffed, dispair or excessive threat indicates the cuff being used against them in some way, to a poie or something.

Otherwise whatever is most epic

Personally, I wouldn't allow a "Cuff attack". If a player who is carrying binders on them rolls a triumph in a brawl, however, could probably be convinced to let them spend it to apply the binders to the target they'd been attacking. I mean, against minions, it's the equivalent to 'taking them out of action' by applying a critical. Against rivals it's a bit more effective then a normal critical, but that's the benefit of carrying these things around with you everywhere.

Unless they have done some kind of pinning or grappling maneuver I wouldn't even allow a check without it. Athletics or Coordination to do that would be fine, or some kind of Brawl check.

I would second this. You need complete control of movement AND limbs to apply cuffs on an unwilling being. Much more difficult then imagined and so much easier with one person per limb being cuffed to be realistic (but yes it's a game so you could ignore that). Multi-limbed beings probably should get a bonus as cuffers while multi-limbed targets would grant lots of setback.

I would use Brawn no matter the skill you used. For both the cuffer and target.

I'd say first a Brawl check to get a grip on the opponent, followed by an opposed Brawn check to twist the opponent's arms around and attach the cuffs. Maybe require a set number of successes to get both wrists, or you'd have to keep trying on the subsequent round.

Yeah, opposed Brawl/Athletics vs. Athletics seems to be the way to go