What kind of pepper are we talking about? If it's a bell pepper (some people call them green peppers -- they're the big ones, not small like jalopenos), then I usually figure about 2 peppers per cup. If the peppers are unusually small or large, then you might have to buy fewer or more.
The smaller you cut up the pepper, the more it will take to fill the cup. Smaller pieces have less space between them, so they pack in more tightly.
I usually lightly pack food into the measuring cup, unless the recipe directs otherwise.
I'd err on the side of having too much pepper. Anything left over can be bagged and frozen for next time.
Hope this helps!