We have used ribbon looped through the wreath, and then taken over the top of the cabinet door. We pin the ribbon to the inside of the cabinet door. It makes a tiny hole, but that's all. Good luck!
Diane...I totally agree with The Kitchen Garten. I use a small tack and it holds well and looks great.
I use Command hooks. Just make sure when you initially attach the Command hook that you wait about 30 minutes before you hang your wreath.
Dollar Tree has wreath hangers for $1. I would just buy a couple of those.
You could do this by taking a wire hanger - cutting it so it's smaller and then bending it to the proper shape.
Pretty ribbon would be another option.
Use a command hook upside down on the back of the door. Using fishing wire attached to the wreath. Hook over the door and onto the hook.