What are the qualifications for a small airport manager?
There are no formal qualifications required to be an airport manager -- it's not a "regulated professional field" in the same way as Doctors, Lawyers, or Professional Engineers.  If a person had the money they could purchase an airport and name themselves "airport manager" of their own facility.

That said, managing an airport has an interesting set of challenges and could probably be described as like being the mayor of a small city with its own road infrastructure (runways, taxiways, and ramp areas), snow removal services, business districts (FBOs, restaurants, &amp; other tenants), municipal services (ARFF), and utilities (airport lighting, fuel farms, drainage systems). The airport manager will also have to interface with federal agencies: The FAA/DOT at a minimum, and likely also the EPA and Homeland Security (TSA/CBP). Working with the local municipality and dealing with local residents on matters like noise abatement is also usually part of the job.
In many ways "airport manager" is as much a political position as an operational one.

Because of the unique challenges involved in managing an airport there are degree programs specifically focused on airport management, and preference will probably be given to applicants with those degrees. Alternatively relevant operational experience (either from running an airport elsewhere or from working in other municipal departments within the county) might be enough to deem a candidate qualified.
There are also professional organizations for airport executives/managers which offer independent certification for individuals.



As a pilot I would say it's advantageous for an airport manager to be a pilot (and in the case of a small airport like the one you describe it would be helpful if they were an active pilot), but being a pilot doesn't really qualify a person in any of the other key operational areas - snow removal, runway maintenance, emergency response, etc. - so while experience as a pilot or controller might be helpful in that it imparts a greater understanding of the operational impact of certain decisions it would likely be viewed as a secondary qualification.