While writing a little screen capture tool (which you can download from Box), I used to following code to capture a region on the screen and copy it to the clipboard:
Rectangle region = …; // the screen region to capture
using (Bitmap bitmap = new Bitmap(
region.Width, region.Height, PixelFormat.Format32bppArgb))
using (Graphics graphics = Graphics.FromImage(bitmap))
{
graphics.CopyFromScreen(region.Left, region.Top, 0, 0, region.Size);
Clipboard.SetImage(bitmap);
}