These are often put out by major industry magazines, or through local professional organizations. Ask around at some of the bigger studios in your area, they probably have several of these directories in addition to their own database of producers in the area. Next to the band or artist, the producer is the most important part of the project, so you need to choose one carefully. Make sure you find a producer that is well versed in your style of music. Make sure you listen to examples of projects the producer has worked on in your style, and have them explain what role they played in each.
Most producers are musicians, and listen to and are familiar with many styles of music.
If the producer is going to be hired mostly for their guidance and to be the objective set of ears, any producer that is familiar with your style of music will probably work well. However, if you need a producer that is going to help with your song arrangements, or even play some parts on your songs, then you need to be certain that the producer can also play music in your style. For example, if you are doing heavy metal music, then a producer whose principal instrument is the guitar, and who has done a lot of metal would probably be a better choice than a keyboardist who usually does po songs, unless of course you are looking to add some keyboards to your music. That doesn't mean that a keyboardist can't be a great heavy metal producer, they just might not be right if you need someone to actually play some parts on your songs, although if they are into the style they probably know guitarists they can bring in if necessary. As with the engineer, you need to be comfortable working with the producer you choose.