They used to sell extra-wide satin bindings specifically for baby quilts. Don't know if they do anymore; I used it once years and years ago (before I knew anything about quilting) and it wasn't too hard. I probably did a terribly amateurish job on it but it worked!
I gave the quilt to a coworker who has long since moved away so no idea how well it held up. Funny to think...that "baby" is sixteen years old now! Woah!