Knockout occurs in 10 seconds. This time can be reduced significantly by hitting with a second Tranquilizer Dart.
In-Game Tooltip
"Knocked out when timer runs down"
Tranquilized is a negative status effect in Streets of Rogue. Once applied, a countdown will appear above the victim. Once it reaches 0, the victim will be Knocked Out. Applying the effect a further time will reduce the countdown time by 8 seconds.