The G4 minis that didn't have Airport already installed lack more than just the Airport card. To add wifi interrnally you'll need the Airport card, plus a small adapter board (often called the 'mezzanine card') and the airport antenna. The entire kit was available as a service part via approved service providers at one time, but is now discontinued. However, it can still be found from time to time if you look.
The part number is M9870z/A and includes Airport and Bluetooth. It's currently listed at
http://www.welovemacs.com/m9870za.html but this looks to be double the usual price it has been seen at.
http://www.mac-pro.com/s.nl/it.A/id.1501/.f?sc=2&category=22 lists it at the usual price. In neither case can it be assumed they are in stock without checking since these are pretty rare these days.
If you get one of these it's not hard to fit yourself, or a local approved service provider will certainly be able to do it for you - for a charge of course - probably around 1 hour labor time.
Alternatively, you could add wifi externally by adding a USB dongle or wifi bridge wired to the ethernet port. USB is typically not a good way to do it where consistent data throughput is needed, but an external wifi bridge would be cheaper than the internal upgrade kit. The downside is that you would not have as easy control of wifi as with an internal card, though signal level might be a little better depending on your specific circumstance.