I don't think the Arabs get a lot of prestige by basically, by a straight money transaction or even via barter, buying spaces on someone else's space program. Be different if it were a partnership they helped build.
For instance, what about a grand coalition of Persian Gulf oil money, Indonesia, Malaysia, Singapore--AND Japan, all making deals with Australia for a launch site or two on her east coast? I think some sites could be found there that have acceptably wide downrange fans from due east to either north or south to a considerable angle--as pointed out by Dathi it doesn't matter if you launch north or south, either way it costs the same and you achieve the same inclination range of orbits, just starting 180 degrees out of phase.
Indonesia itself might seem to offer launch sites but there are always going to be legions of small (and not so small!) islands in the downrange fans. If they aren't going to launch from the Australian coast they are looking at some island in the big empty of the Pacific, and having to tote all the logistics from engines and fuel to toothbrushes out there.
My computer is overburdened again and I'd have to shut down and reboot to dare load my map program, but perhaps the Philippines also have some fair potential launch sites?
Anyway, this coalition is:
Arab-Islamic (Sunni!) money and a certain amount of technical knowledge of their own;
Japanese high-tech expertise;
Two Islamic (again Sunni) southeast Asian nations which are in the process of developing their high-tech sector;
Another quite rich and high-tech Chinese colony throwing in, like Japan, for the money and access to profits, as well as prestige;
A pretty solidly high-tech if in population terms small but rich in resources Anglo country getting funding to develop a launch site on their soil, one they can also market to American, European, or post Soviet collapse if that happens, even Russian rocket makers as well. Unlike being in ESA (and if everyone is clever, there's no reason they can't stay in ESA too) the Australians in this partnership the big stars in terms of providing the launch sites and local logistical support (from machine shops to groceries) in the region rather than being on the far side of the world, ultimately to be bypassed in favor of a South American site much closer to Europe.
But if sheer money can buy anything, the Arabs might be tempted to do without the various East Asian (even if Muslim) and Australian partners, and focus on simply training up their own people to do the job themselves. Then as I said, they'd need a launch site. I said Somalia rather than Kenya because the Somali coast is firmly Islamic and in fact if Oman is a partner, was a onetime colony of that power. Also, the Somali coast is relatively depopulated and Arab money will buy a lot more political influence in that impovershed country than in Kenya or Tanzania, and with less controversy.
Perhaps meanwhile all the eastern Indian Ocean (and west Pacific) countries I mentioned--Malaysia, Indonesia, perhaps the Philippines, partnering with Australia for launch sites and Japan, Singapore and perhaps Taiwan for high-tech expertise (surely Australia would be included wearing that hat as well) can also go it alone without Arab money?
Of course the truly cost-effective thing is to simply buy in to someone else's functional program, a little sharing the costs and risks can buy benefits out of proportion. But not glory.
And so OTL Japan has indeed had her own program, and I've read of Singaporian schemes. If they pool their efforts they have to share the glory but the achievements might be considerably more splashy, sooner.
That said, some countries from the arabian penninsula will be included in the Spaceflight Participation Program on Spacelab, and the program successes are enough that it's likely to roll over into whatever's next for NASA--so they're already getting the prestige of astronauts in orbit for not much in the way of money. Maybe once commercial spaceflight comes about as more of concept you might see more from Arabian private individuals (the proverbial "crazy Sheik" from earlier), but that's a story for another update.