How to Kill Armadillos with Poison
To put it simply, you won't be able to kill an armadillo with poison, short of injecting it into the armadillo yourself. Armadillos eat food from the ground and won't be tempted by poison baits that may be safe to use on other nuisance wildlife.
You may see products that claim to get rid of armadillos in local stores that sell yard and garden supplies, but they are phony and are not proven at all. Do some research and read reviews about these products to find out yourself it's a quick way to lose a $20 bill. Don't be fooled by armadillo poison, do the right thing and attempt to trap or exclude the armadillo.
Armadillo Lead Poisoning
Some cities permit the shooting of armadillos, but it may be illegal to disharge a firearm within the city limits. There are many legal caveats to killing wildlife with guns in the United States, so be careful that you aren't getting yourself in trouble over a little armadillo.