You probably could use Minky for the binding but I think it would be a challenge because it is so stretchy and slippery. I have never done it. If it was me I would go out and buy a 1/2 yard of any coordinating color fabric---it doesn't have to match exactly to what you used in the quilt. Just find a solid or stripe with your colors and use for the binding. I have seen lots of cute quilts with totally different or contrasting fabric bindings, even like a black and white stripe binding on a color patchwork quilt.