If you're machine quilting, try drawing your stencil on to freezer paper and then iron the freezer paper to the quilt. It can be machine sewn through with little trouble. The freezer paper tears away pretty easy, or it can be dampened to release a little easier.
Hand quilting might be tougher. I've used tissue paper with a drawn pattern on it and stitched through both quilt and paper, but I had to use a hoop to hold it all in place. Not sure how well this would work on a border, tho.
I've also had good luck using basting thread to outline the border area from the front of the quilt, then centered and drawn the stencil on the back. You'll be quilting from the backing side, so it requires a bit of care to get those front stitches looking as nice as the ones on the back. Also works best if the backing fabric's muslin or a light colored fabric easy to see the marking on. Your backing seems light enough, from the photo.
Good luck with whatever you choose to try. Your quilt is lovely!