I've done a couple of baby quilts using a fancy stitch. A couple of things that really help is to press the binding seam nice and flat before you bring it around to the other side. It helps it stay that way while you are working on it. I also pin it a lot! Every couple of inches. You could also try using washable elmer's glue to hold it while you do the stitching. Then wash it to get the glue out.
Oops, almost forgot ~ I use a walking foot on the binding.