What is the fastest way to build an alanine scanning library?
The fastest will change as time passes and better technologies are developed. 

I think the fastest method existing at the moment is Shotgun Mutagenesis (provided by Integral Molecular Inc).

This does not employ any new method of doing that. They just provide a set of plasmids, that has all the possible mutations. The set itself is generated by automated DNA synthesis.

So if you don't have a DNA synthesizer with you then simply order the kit from the company.