Are you talking grass carp, or common carp?
If the fish are right at the surface, try using a shotgun with coarse shot, such as #4.
Shoot slightly low to compensate for the refraction of light. For example, if the fish are 6" or less under the surface, hold at the bottom of their body line at the back of the head. Make sense?
Get a bow hunter to come out and shoot some with specialized bow fishing arrows and other equipment.
My grass carp swim right among the feeding trout, bluegills, green sunfish,etc. without disturbing anyone. And, they are big-36" long.
I have no idea if your bluegills would be leery of common carp.
