If the eyes are as big as buttons why don't you use fusible applique and applique them on then do a tiny zig zag stitch or straight stitch along the edge to hold the applique down. Or you can use felted wool or fleece or minkee, none of which fray and will add some interesting texture for the baby. Or find a friend who has an embroidery machine that can maybe do the eyes for you in machine embroidery.