I would rule than if the number of tranq shots that hit is more than half COM there is a 50% chance of OD. More than CON, the target OD unless medical help is available within a few minutes.

I would do this regardless of the caliber of the shot. Sadly TNE doesn't provide proper rules for dosage on tranq rounds based on TL or caliber.

I like your idea of basing the number of hits against the targets CON.  I remember reading in a Challenge magazine(I think) that the PCs were asked to hunt down some large animals and were given large tranq guns and that there was some mention that shooting people could be "dangerous.   I think that most military small arms are designed to shot people sizes targets so the amount of tranq in the tranq rounds would be enough to take down the averaged sized person, about 80 kg body mass and that larger bullets would have more absorption agent,to better penetrate the skin.  Civilian weapons are used for hunting animals.  Here how about as a rule of thumb that 5mm rounds have half the normal amount of tranq that a military weapon would, 7mm weapons would have the same amount, 9mm weapons 2 times a military weapon and 12mm weapons 3 times the amount a military weapon has.  
     Skaran your idea that tranq is a poison reminded me, once we substituted poison for the tranq, an assassin got his hands on one of Aubaine's infamous spiked glow fish (level three poisoned spikes) and used his chemistry skill to refine the poison (good roll playing, I allowed the level of poison to be increased to level P-5 due to a n outstanding success roll).
     Tranq is fast acting and quick to recover from and I want to keep these features, but I think that multiple hits are going to put more tranq in the body and I think that someone would be knocked out for a longer period(take the square root of the number of tranq rounds that hit times the 1D6 minutes.  In the case of our pirate had he lived (he didn't) would be down for  1 to 6 minutes x 3.
     Thanks guys I appreciate the help.