This is from Andi Parkisnon

This is from Andi Parkisnon RDMS of Intrapet Imaging in Baltimore, MD:

Here’s the secret to bunnies—have an experienced holder.  Bunnies have a weird “trance” reaction to having their eyes covered.
  So, you need to gently get them onto their back in a trough (gently because they can break their backs

From Rachel Brilhardt RDMS of

From Rachel Brilhardt RDMS of Intrapet adds to this:  

Perfect description but to add that rubbing their chest while covering eyes will help get them into trance. Also be careful not cover nose or mouth when covering eyes.