Got one a few years back when I was in Doha (although even then all actual applications were via an office in Germany - you pay DHL charges both ways).
Basic requirement was a letter from employer as others have said. Since I couldn't send my existing valid PP with the application (as I guess most of you can't either) I also needed an attested copy of it. The Embassy arranged that - for a fee.
All went smoothly if not cheaply - 2nd one took about 2 weeks to arrive.
BTW the above applies to UK Passports - other countries may have their own rules.
Beware - it is rumoured that K.S.A. view the holding of a 2nd PP as illegal. Tho' it isn't. Anyone know more about that aspect?
Last edited by Dubaian; 18th Sep 2014 at 07:12.
Reason: Additional Info