Alas, urethane glue didn’t hold the eye marbles in the garden dragonfly ornament for very long. Although the cured glue had a wonderfully smooth surface where it contacted the balls and it had plenty of contact area, that wasn’t enough.
This time, I used acrylic caulk that should stay gummy enough to maintain a good grip:

The next step, I suppose, will be to drill a hole in each ball for a stud and epoxy the things in place…