Hand embroidery would work. Also check out your machine's built-in stitches. I think I've done eyes using two half circles, or maybe an eyelet. You will probably need to use some stabilizer underneath..

Hand embroidery. A nice way to make round eyes is to first make 5 stitches from the center out - sort of looks like a star. Then sew over & under those stitches in a circle working from the center out. Because there is an 'odd' number in the star the circular stitches end up looking woven. You can then add details if desired.

Another way, if you want it the eyes from fabric and they aren't too small, cut a circle bigger (about 2x) than the finished eye. Run a basting stitch around the outside edge and then pull it in so it makes a "bubble". Then squish it flat and stitch the outside edge down.

I do it that way, too, but put something inside to pull it the thread against, like a plastic circle from the heat resistant template plastic. Then you can iron the dickens out of it and remove the circle.

Thanks for the suggestions. I tried my machine stitches and didn't like how they looked. My hand embroidery eyes were also ugly. I ended up doing the basting stitch method and while they are a little larger than I really wanted, I liked the overall look, so the eyes are DONE!!! I will get pictures posted soon. Thanks again.

Sue