Pahlava simply cannot build irrigation in those cities without a proper government building, which are gov1 or gov2. Well, Pahlava do have a principally gov1+gov2 building, which named "Parthian Reform Government", but it just can be built in regions that have "pahlavahome" resource, while none of "desert"-resource-regions have that.

To build irrigation, you have to do it with trick, using loophole in EDB data system. You have to “steal” the former faction gov1 and gov2 buildings, and then you can build irrigation.

This thread may interested you:

https://forums.totalwar.org/vb/showt...my-governments

I am using gov1 and gov2 of Saba, Ptolemaioi and Qartadast in those cities to build irrigation, but not in Gerrha, coz in my campaign, it only has Gov4 of Saba to begin with.