All my bears either have buttons safely sewn tightly on for eyes, or I use safety eyes. Below I've added some photos so you can see exactly how these work.
They are comprised of a plastic pin-like eye, and a washer with a hole in, with two teeth.
It is only possible to push the pin through in one direction, and then you can't pull it back as the teeth dig in.
After this is attached through the felt and the sock, I then stitch the felt surrounds onto the sock.