Where can I find designers (except freelancers) on hourly basis for web design?

As a retired graphic designer it is not clear why you say "except freelancers"? As near as I can tell a freelance graphic designer is exactly what you need. You indicate that you want to a designer on an hourly basis and that is OK if you want to use the designer full-time for a matter of weeks or months. If you need a few projects done, that is normally only done of a per project freelance basis and normally quoted by the project rather than by the hour. If you do find people willing to do small projects for an hourly fee, they are much more likely to be amateurs doing amateur quality work.