When you are working around curves, you must use bias binding. Straight-grain fabrics will not bend around curves without puckering.
As you apply the binding by machine, at the highest point of the curve (that is closest to the inner part of the quilt), take one horizontal stitch before descending to the next curve. In other words, come up the curve, turn and take one stitch parallel to the body of the quilt, turn and then descend into the next curve. Obviously, you will have to attach the other edge of the binding by hand.
Also, I would keep my binding narrow, about 3/8" or less. Any wider than this will cause too much bulk at the inner points.
Hope this helps. Suzanne