How do you create a parking permit on post?

Unless it's a legal prohibition (i.e., handicap parking, etc)., any restrictions on parking are done by the property owner. If your unit is responsible for the buildings, parking lots, etc. then the unit commander could implement a parking restriction policy.

However, that's not likely. The most probably situation is that everything is under the control of the installation commander and any parking restrictions are done by his policy. This means that you would have to get those restrictions approved by him.

I have seen instances where the post commander has delegated policy management of sections of the base to those commanders responsible for those areas, but usually those are restricted access locations.

Since you tagged this question with Fort Shafter, I assume you're asking regarding that installation. US Army Hawaii Regulation 190-5 (US Army Hawaii Traffic Code)* is applicable to all US Army installations, facilities or work sites in the State of Hawaii.

Specifically chapter 4 goes over parking and there IS (section 4-9) a discussion about reserved parking and how to get any designated (spoiler: it doesn't appear from the reg that you can section off parking for "unit personnel only" ... only senior individuals).

The Directorate of Emergency Services Reserve Manager at DES Operations Office is the one that oversees reserved parking.
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* https://home.army.mil/hawaii/application/files/5515/8026/3156/USARHAW_190-5_09_May_2019.pdf

Your best course of action would most likely be having your sergeant major reach out to their sergeant major and to see how they could facilitate are you better solution for the quality of life of their soldiers.