Sure. Only one place sells regulators in Friday Market and that are DUPLA brand Regulators and at nearby mall they sell easy co2 regulators. But their prices are ridiculous. I heard there is a store in Salmiya from an employee at roc. Apparently that store sells CO2 regulator with Co2 tank that they buy from ROC.
I'll also ask the shop that I found the metering valves at about the regulator. He has all types of valves/pipe equipment so he should have regulators as well. I think inert gas regulators (argon etc) should work with an adapter (do they?)
Worst case scenario we'll go around all the welding shops in Shuwaikh asking if they have co2/inert gas regulators they want to sell.
As for the solenoids, they're not really really necessary. I'm not even thinking about getting one since it's hard enough to find the rest. Btw Friday market is an excellent place to get Co2 tanks. Got an aluminium 8kg or 10kg CO2 tank that's still certified and full for I think 8kd. I'm going tomorrow to buy all compatible regulators before you :P I'll tell you if I found any