1. I don't think there are discounts available (currently) to apply to any AP purchase.
2. Renewal of your AP within a small date range from expiration used to get a $20 renewal discount. Not sure if Disney has discontinued that practice though.
3. If there were discounts available (see point #1), I'm sure Disney would not let you combine them with their renewal incentive (point #2).
So ultimately your best shot at any discount will be if Disney still provides the AP renewal discount.
I purchased mine at our city employee store just before the rates went up. I saved more than the renewal discount that Disney offers. Just check with your HR Dept, I guess even AAA, but I have not tried that one.
I got a new (not renewed) SoCal Select AP in person at an AAA office in April for 261.50, a slight discount from the then price of 269. If Disney doesn't give a renewal discount, and the 7.50 is worth it to you, you might let your AP expire and get a new one just before your first trip after expiration.
Here You Leave Today and Enter the World of Yesterday, Tomorrow, and Fantasy.
“To all who come to this happy place; welcome. Disneyland is your land. Here age relives fond memories of the past...and here youth may savor the challenge and promise of the future. Disneyland is dedicated to the ideals, the dreams and the hard facts that have created America...with the hope that it will be a source of joy and inspiration to all the world.” - Walt Disney, Disneyland Opening Day Speech 1955
The renewal discount is now $40 for Premium, $20 for Deluxe, and $10 for SoCal/SoCal Select. I'd say on the more expensive passes, you're better off renewing, unless you'd like to take at least a 6-week break or so from the park, while the AAA rate is close enough to the renewal rate (the same, for the SoCal pass), that you'd probably come out ahead with AAA unless you plan on going more or less immediately after your pass expires.
Of course, there are other considerations: mainly, the hassle of a special trip to the AAA offices (I don't believe this offer is available online, and last year when I bought my pass I found my local AAA office rather inefficient), and the fact that with AAA you aren't eligible for monthly payments.