This is a dilemma. The first generation (802.11b/g only model A1084) Express requires AirPort Utility 5.6.1 or a similar, older version of AU. Mountain Lion will refuse to install it. What to do?
As it turns out AirPort Utility 5.6.1 runs perfectly fine on Mountain Lion. If you had the foresight to have archived it somewhere (such as with Time Machine or equivalent) you can simply copy the app to your computer and use it. The problem is that the installer package will refuse to work on a Mountain Lion system.
If you don't have an already-extracted version of AU 5.6.1 there is a solution: you simply need Pacifist to extract the app from the installer package. I also found another technique described on this page: