Recently, I started a competition with a friend of mine to see who can build the most accurate airgun. We will be firing at targets from 10 to 50 meters (with 10 meter intervals) to see who can get the best accuracy and/or grouping. We agreed on three regulations: Sub-15mm caliber, no CO2 and has to be a portable design. The plan is, obviously, to completely obliterate him.
The question
What kind of ammo should I use to get the best results?
Here's a list of properties I'm looking for:
- Can reach out to 50 meters, while being driven by a spring and piston*
- Ballistics that can be predicted reliably** (no matter how complicated)
- Manufacturable from parts/materials that can be bought or easily molded
- Will be fired out of a barrel without rifling
- Preferably drag-stabilized rather than fin-stabilized
- Preferably 6.0 or 8.0 mm caliber, but up to 15.0 mm
- Preferably able to pierce a piece of paper at 50 meters
Some more information
Both of us will likely use a spring mechanism* which will drive a piston. Alternatively, I also thought of using rubber bands in combination with some sort of pulley system to drive a plunger through a piston.
I currently have .12 and .20 gram BB's*** (6 mm). I know that the .20 ones could possibly reach out to 50 meters without much trouble, but being light and spherical, they will also be hard to predict. Saboted BB's could be used to prevent any kind of spinning.
And finally, I'm extremely intrigued by drag-stabilized projectiles. I could cast the tip out of whatever and stick something like a foam or paper cilinder on the back. This will allow me to make heavier projectiles for the same caliber (but increases parasitic drag).
If you genuinely do believe that there is absolutely no possibility that any of the requirements can be met with a spring-propulsion system, you could also recommend me an ammo-type that can be used with compressed air (preferably under 8 bars of pressure).
Thank you for reading and I hope you guys have some good recommendations for me!

Notes
* Please don't try to discourage us about this.
** Some examples of external effects I could compensate for with calculations: Gravity, wind resistance, windage, altitude, temperature, humidity, magnus effect, parasitic drag (for non-spherical projectiles) and coriolis drift (probably negligible).
*** BB's are not sold in my country, so just assume these are my only options.