That's a good question. Even here it's a bit difficult to find language schools as they don't really advertise, you need to ask around. I checked on the net for Riyadh. there are a couple of links, but they're a couple of years old.
Riyadh Institute Offers Arabic for Non-Arabs
Here's a link from a forum. Not sure how helpful it is. arabic language course in Riyadh - any advice? : British Expat Discussion Forum
Worst case scenario, you could do what I did - pick up a home study course that has a CD and book and do it on your own time at your own pace. Let us know how you make out.