If you have the nose cone, tape and string is all you need.
Attach and remove tape until the centerline axis of the nose cone is perpendicular to the floor. The intersection of the imaginary line that goes from the string into the nose cone and the centerline axis of the nose cone is the center of gravity. This is true regardless of a solid or hollow nose cone.
To approximate the center of gravity of a nose cone that you do not have, you calculate volumes in sections of length increments (say from 1 mm to 1/4", depending of the accuracy desired). Assuming a homogenous and solid nose cone, the center of gravity is where the sum of the volumes from the tip to point "x" equals the sum of the volumes from point "x" to the base of the shoulder of the nose cone. If the nose cone is hollow, then you have to add a step of removing the volume of the hollow portion for each section.
Greg