It’s great that you’re being thoughtful about the process! To communicate that a candidate doesn’t meet your qualifications without violating fair housing rules, you can simply focus on the criteria rather than the individual. Here’s an example of what I've used if they don't qualify based on what's on application.
Subject: Status of Your Rental Application
Dear xxxx,
Thank you for your interest in the rental property at xxxxxx. After reviewing your application, we’ve determined that, unfortunately, we are unable to move forward with your application at this time, as it does not meet our established criteria for income and (other established criteria)
We appreciate the time you took to apply and wish you the best of luck in your continued search for a home.
Best regards,
This approach is neutral and objective, focusing strictly on the criteria, and avoids discussing any specifics about the applicant’s personal situation. By emphasizing your qualifications as the basis for your decision, you steer clear of potential issues related to discrimination.