Connecting genie go to a AT&T 2wire

Not a Genie specifically, but I've seen issues with certain wireless encryption types and certain devices, so if you're having issues, try changing it. Look for something like WPA mixed mode. Or try WPA2. Or if it's WPA 3DES, try WPA AES, etc. Just try different settings until the Genie will connect.

Or you could run a cable to it which is really what I recommend but I know you won't do that.

No lie, I had both att and directv techs tell me to get a different internet provider and a different router because it's virtually impossible to connect and keep connected. I have no other internet options so I just said screw its and left it alone after about three weeks of messing with it.