He needs 6 screws at a time, and the goal is to save time compared to counting manually. I'd guess that 7 would probably be fine occasionally -- maybe even 8 from time to time if the process is fast enough. I'd further guess that 9 screws is a non-starter (screws are inexpensive, but 9 represents 50% waste, which is quite a lot).
The lower limit is hard-set at 6 because the kits that he's producing and selling require exactly 6 of these screws for end-user assembly.
A small cup that would reliably scoop out at least 6 screws and no more than 7 or 8 screws sounds like a simple and elegant concept.
What does this cup look like? Is it faster to use this cup than counting by hand is? (Is it faster than the reproducible screw counter that he's already built?)