In my experience, live trapping them is fairly easy.
Ive found that setting an unbaited live trap, then build a "funnel fence" at 45 degree angles from each side of the trap entrance to a length of 8 to 16 feet is the preferences method in my area of Oklahoma.
The funnel fence only needs to be 6-8 inches tall.
Armadillos tend to like edges and have poor eyesight, so they will eventually find the trap during their forays through the property.
Disposing of the armadillo is a different matter all together.
I personally give the critter a final "swimming lesson" by placinging the whole trap in a compost tea tank for 30 minutes and then compost the whole carcass afterwards.
As for protecting a garden, I've found the surrounding the garden with a 16 inch welded wire fence, buried 4 inches in the ground tends to be quite effective.
When TPTB take away a persons LEGAL ability to produce for themselves, then I will be a criminal and you will get to support me
I agree on trapping. In most of the Southeastern US, they are invasive and cannot be relocated. So, I spend a lot of my time trying to educate people that armadillos are not all carriers of disease and are good meat. Being a Texan, I can only hope you have had armadillo pie and know just how very god this fascinating and wonderful critter can be. I love armadillos. They are cute, interesting and just plain cool. But, above all else, for me, they are good to eat. Like wild rabbits(that ca also carry disease) , take care when dressing them. Cook thoroughly.... and enjoy something most folks can't or won't experience! I like cage traps for the, but a medium size... like 220, body grip will work just fine.... a "colony" style trap may work even better, especially if blind set.
"Them that don't know him won't like him and them that do sometimes won't know how to take him... he ain't wrong, he's just different and his pride won't let him do the things that make you think he's right"