Quite simple this one Simon.
It avoids all racist, religious arguments.
Don't advertise any possible fails. pet's, kid's, smoker's, white, black, etc.
Arrange a viewing, ask them the above 'obvious', questions

Yeh, I'm black

Tell them you'll be in touch.
If you don't like the viewers of 'your' property,
get back in touch and tell them they weren't succesful in their application.
Simples

'You', don't need to explain to them why they were declined the place.