I am trying to figure out a way to schedule working Saturday's to play a business open greeting on the 1st and 3rd weekend of the month and a closed greeting on the 2nd and 4th Saturday of the month. Does anyone have any ideas?

If it is not possible to schedule the AA like that is there a way to manually open business on the Saturday's we are here and close it when we are leaving for the day??

Use the holiday option in the Auto Attendant. You didn't mention what system you had so I'm responding as if you have a current system, like a BCM, Norstar with Callpilot. You can choose which days are days you want the greetings to be played. Record the greeting under the company greeting, and use greeting 10 for the 1st and 3rd weekends. and use greeting 11 for 2nd and 4th. The drawback is that you need to specify
the weekends under the holiday option. Good Luck.