Paralytics must be delivered to an individual with great precision, or they are either ineffective or fatal. So the idea of delivering a paralytic via a paintball, even if it was carried through the skin via DMSO or something similar, would still have to be delivered in the correct amount, or the target will stop breathing. This is why anesthesiologists are paid so much money - it is their job to keep the patient unconscious during an operation, but also keeping them from dying from overmedication.
Some years ago, a Chechen group took over a theater in Russia. The Russian special forces counterattacked, after delivering a 'knockout gas', believed to be an opiate derivative, through the theater's ventilation system. About 100 or so out of 400 people held captive died by suffocation, not immediately, but because the rescue people who came in afterward were not told to keep the hostages upright. Those left lying down suffocated from an inability to breathe properly.
At least with current med tech, there is no way to 'knock someone out' without knowing precise information on their weight, body mass index, age, current health condition, and even how much they had to eat recently (might puke and choke on it).
As an alternative, it is known that some sounds played in sufficient volume, can reduce the target to a severe state of nausea and even unconsciousness. You might think about a knockout gun along those lines... plus earplugs for the person using such a device.