Without any additional info, I'd suggest just trying it. This is what prototyping is for! Create a system that will emulate the function of the mechanism that you want on your robot and then make changes until you get it right.
If we have the same system in mind, I'd bet you one CIM would be enough. I would, however, caution you against conveyor belts as a shooting mechanism as they are very difficult to execute in a way that is reliable.
I noticed that this is your first year as a team. If you are looking for designs that are proven to work with track balls take a look at robots from the 2008 game Overdrive.
The link to the wiki on it is below
http://en.wikipedia.org/wiki/FIRST_Overdrive
For conveyer belt designs look at robots from the 2012 game Rebound Rumble, wiki listed below
http://en.wikipedia.org/wiki/Rebound_Rumble
Good luck!
Feel free to ask any questions that you might have
Garrett