Script 1:

"Hello. Lately, I've been really having to stretch my finances to make the monthly payments on this credit card, and I need to reduce the interest rate somehow. It would be convenient to keep the balance on this card, but I have some other options that could really save me some money - a zero interest balance transfer offer is sitting right here, for one. Could you reduce the interest rate on my account to, say, 9.9%?"

Source:

http://lifehacker.com/5167254/make-a-phone-call-that-lowers-your-credit-card-rate

Script 2: LearnVest offers a checklist and script for convincing your credit card company to lower your APR, from gathering offers other companies mail you to asking specifically for a "credit account specialist" when you call. 

Be polite yet firm, and ask open-ended questions instead of any that can be easily answered with a "no." Case in point: "Do you think that you can lower my interest rate?"

Consider using this script:

"Hi, my name is _____. I've been a good customer of (current credit card company) for (number of years), and I make my payments on time, but my APR is too high. I have offers of (x) from (competing credit card company A), and (y) from (competing credit card company B). I've had a good experience with you, but I'm considering switching. I would like to have my APR lowered." [Note: Ramit Sethi has also gotten good reviews for the script included in his book, which is also available via this $1.99 iPhone app.]

If they offer you just a point lower, but don't get you to your target rate, say, "Can you do any better?" If it's the best that they can do, move on to the next step [talking to a supervisor].

Source: I Want to Negotiate Down My Credit Card APR | LearnVest