Naturally ridding my backyard of green ants and meat ants?

Agree with Diatomaceous Earth (DE). DE is actually the fossilized remains of ancient sea creatures. It feels like fine talc to us, but at the microscopic level, it is like needles. Those needles pierce the exoskeletons of the insects, causing them to dehydrate and die. It can be used indoors or out. I put it in a plastic ketchup bottle (the kind that restaurants use) and run a strip around the foundation of my house every spring and autumn. It keeps the bugs out. The only caveat is to make sure you don't breathe the dust.