Yes, hand the object from three points. If the object is an extruded object (like...a 2-D object with constant cross section and some thicknes), then you simply hang the object from three points and draw a vertical line from that point straight down. Where the three lines intersect is the CG (in the center of the body of course). If your three lines intersect to form a triangle, then simply find the center of the triangle to find the center of the body.
Try this link for a lecture I remember for a lab that was on finding an objects center of gravity and moment of intertia: