There are several ball designs that fit your needs (and are commonly used for GBC machines) - a selection :
- Ball, Sports Soccer Plain, and their various multi-colored variants (eg. Ball, Sports Soccer with Standard Pattern) (14.2 mm diameter ; 1.75 studs)
- Ball, Sports Basketball with Standard Black Lines Pattern (14.2 mm diameter ; 1.75 studs)
- LegoBall, Bionicle Zamor Sphere, and their various multi-colored variants (eg. Ball, Bionicle Zamor Sphere with Marbled Yellow Pattern) (16.5 mm diamaterdiameter ; 2 studs) - note these aren't as commonly used for GBC machines as the others, but I've included them since they fit your size needs better.
