How to make Koopa (ovular) eyelids?


I’m making a little lizard guy and I’m trying to get his eyelids down, but I can’t figure out how to make them work for his ovular eyes so that I would be able to set it all up for animation.

This is essentially what I’m trying to achieve:

And this is a screenshot of what I currently have:

I currently have an enlarged version of the eyeballs that has been partially deleted and then added a shrinkwrap modifier so they’ll wrap around the eyeballs, but the results are not very good :confused:

Use shape-keys instead of an armature.