Scrane,
Many of the big bore air rifles have plenty of power to take a deer with a heart/lung shot. Most people simply have no respect for what 175+ foot pounds of energy represents. For example, a Benjamin Bulldog will break a brick in half with a single shot (145 grain Nosler Extreme). I learned this the hard way in my backyard shooting range. It was set up with a box with crushed cans, double layer of bricks and a wooden backboard, followed up by a fence. My 40 foot pound air rifles just makes little chips on the surface of the brick, and after a lot of shots (in the same spot), bores a hole through the brick by comparison. With the Nosler, around 200 foot pounds energy, projected penetration in a critter, is around a foot. This level of power is greater than a .22 long rifle (100-120 FPE).
Like many states which allow air rifles to be used for "big game", Arizona imposes a minimum caliber of .357. Check your local hunting laws to confirm compliance before investing in a Deer air rifle (some states require .45 caliber or larger).