Here are a few different ideas for you! https://www.wikihow.com/Hang-a-Quilt
This relies the weight, usually you are best to use Rope like Clothesline because these are too heavy for a Braided Fishing line
You can frame it and then hang.
Here are 4 different ways to hang a quilt: http://www.right-sides-together.com/four-ways-to-hang-a-quilt/
Val....Buy a nice curtain rod and attach to a piece of wood. You can stain or paint wood just depends on the look you want. Make sure you find 2x4s and put on all. Fold the quilt and drape over rob.
You should NEVER drape a quilt over a stained piece of wood....the stain will transfer to the quilt! Sew a sleeve onto the top of the quilt and then hang it...no direct sunlight....