Little beady eyes in copper foil

My current copper foil project has a lot of little birds that are
about 2 1/4 inches long. I had originally planned on creating small
black eyes on the birds by applying a tiny dot of puff paint to the
finished project for each eye. Now I am thinking that this would not
be as permanent as I would like. I need to create six eyes total for
this project.

I thought about drilling a small hole, putting a piece of copper wire
in the hole, and then adding a dot of solder. But how to drill the
hole...

Where could I find a diamond drill bit that is only 1/16" to 3/32"?
Is there such a thing? I thought about using my small engraving bit,
but that didn't seem like it would work.

If anybody has any thoughts, suggestions or ideas on how to handle
this, please share!

Thanks,

Jeff