In my several years of experience, finding a job as a sorority house director isn't hard; it's finding the right campus or other conditions that's harder. Some people may have a preference for their Alma mater while others may want to move to a certain state or region to be closer to family.
With a few phone calls, you can easily find out if a campus or sorority has any openings.
If you're interested in a certain school or region, call the Greek Life office at the school. They usually know if there's a position open in one of the houses. Occasionally they may know of other schools that have openings. Sometimes the school may ask for a resume to keep on file just in case there's an opening later on.
On the same note, you can also call any one of the 26 sororities in the National Panhellenic Council and ask to speak to either their property management team or housing corporation. Again, you just ask if they have any house director openings. From past experience, they like to collect resumes for openings that come available, especially if you're willing to move.
You can also utilize job search sites like Indeed.com and use the keyword "sorority house director."