Gardenville recommended Beneficial Nemitodes to get rid of grub worms (which
is what armadillos are looking for). You can buy them at Gardenville or Red
Barn. They come in these packages of dirt that you mix with water and spray
on your yard.

It worked for us -- no more grub worms.

The armadillo will not dig holes if it fails to smell a grub - maybe
an earthworm. If you eliminate those then the armadillo will
naturally move to a yard with a better grocery store. So you could
try treating your yard for grubs. Don't they have a biological agent
now to do that?