mAirList can either use version 7.x or 8.x of the PostgreSQL client library. Version 7 is recommended because it is more stable, even when using a more recent (8.x) server version.
The required library is named “libpq74.dll” and should be included both in the Professional Edition setup as well as the Zip distribution. Or you can download it from here: http://www.mairlist.com/download/misc/libpq/7.4/
You also need to set the “Protocol/DLL version” field in the mAirListDB configuration to “postgresq-7” which is the default.