That is a really good question! We've written at length in various articles on
http://www.studentplatinum.com about how to call your credit card company to get your interest rates reduced. I honestly had not thought much about store credit cards and I'll tell you why - I stay away from them.
It wouldn't hurt could call them and tell them you are going to not use the card or even cancel it unless they offer a more competitive APR. My guess is they can't or won't which is why I don't have one. I used to have a few store cards and over time they just didn't offer as much of a benefit as a traditional card so I phased them out. I realize your question is if there is a way to get them to do it and I'm not sure. I'll get somebody here with a store card to volunteer it and we'll call and report back what happens. Theoretically they should work with you because using their credit card ensures you will buy their merchandise and so the APR is a bonus on top of their margin on products.
In my experience store credit card limits are low and APRs are high when compared to a traditional credit card. So why do people get them? Generally they are easier to get than a regular credit card for the reasons I just mentioned. They are eerily similar to a credit cards for people with poor credit (
http://www.studentplatinum.com/poor-cre ... /index.php) and that should tell you all you need to know about them. Even if you have poor credit, go for a credit card for people with poor credit because at least you can negotiate rates as you prove that you're responsible.
If you read this and have a store credit card please let us know your experiences with it and about any attempts to lower your APR!