Thaz,
I'm actually researching this q right now and happened to stumble upon your post. Good news is that this question is not settled law in AL, and what comes to most people's mind when they hear of an "open account" (what qualifies for a 3-yr limitation) is a credit card. That being said, there is legal authority that could be interpreted both ways. Go to your local law school and look the following cases up to argue your point in court (I'll be back with more help once I actually have this written):
1. Wyatt v. Bradford & Company, P.C., 456 So.2d 822 (Al. Civ. App. 1984)
2, Ayers v. Cavalry, LLC, 876 So.2d 474 (Al. Civ. App. 1984)
Also, do not admit that that you owe whatever amount they are alleging. An "account stated" requires that you and the cc co agreed at some point as to the amount owed (it was liquidated and undisputed). Think of some reason why you don't think you should have had to pay it. They will also say that you consented to the amount by not responding to the bill (implied consent) you were sent after they canceled your account. If you gave them any kind of response that indicated that you were disputing the bill make sure to mention that to the judge.
They may also try to argue that this is not barred because the SOL and/or the characterization of the debt is substantive law governed by the law of the state agreed to in the k (usually N. Dakota, where this would definitely be a 6-yr limitation). I doubt they send a lawyer competent enough to make this point (no offense, but your debt is too small for them to spend the bucks on good counsel), but if they do, let me know. This issue is much more complicated.

