If someone has a decent lungful of air when the choking starts, it could take several rounds. Chances are, however, that the person won't have that full breath. I'd consider basing it off the character's CO score/10 as the number of rounds until passing out occurs. It's not truly a damage-dealing type of effect, as once they wake up (if the choking stops before death occurs), they will likely have a headache, but usually no significant damage, unless a wire or fine cord was used.
If using a cord, I like the idea of a grapple attack. If using an arm or a large cloth, I would consider the MA sweeps table. Modify the attack roll generously in favor of the attacker (i.e. flank and rear bonuses), and use any even mildly connected combat skill to give a decent OB, despite the table being used.
Also, if an attack succeeds, I would treat the defender as being stunned for that first round, out of sheer surprise, regardless of the attack result. That should greatly limit his retaliation options for that initial round.
Also, once the garrote is in place, I would allow the attacker a bonus to ambush or crit modification each round, as well as a significant decrease to the defender's OB for any attempt to break free. I would allow the attacker to continue to make attack rolls each round, with 0 effective DB for the defender (unless wearing a gorget) as the garrote is already in place. Any crit result that generates a stun or an incapacitating result would speed the end.
If using the attack tables, it may be that the damage accumulation from successive rounds of attacks will end the matter long before the CO/10 rounds count is reached. In that case, I would have blackout occur when hits was reached, and death when CO/10 + 5 rounds was reached. If you don't plan to kill, I would treat the damage from this attack as soft damage, all but 10% recovered within an hour of waking up.
