I actually have never had a parent ask me that question. I do not have anything to offer but my experience with my own family and the volunteer work I've done in elementary schools. However, I do tell parents that I am a certified teacher although I have never taught in a classroom apart from my school placements as I can't get a job in the area I live in. I know it is not ECE but I think it lets parents know that I do know a bit about children and creating programs, but really, I dont think it sets me apart from anyone else who doesn't have their ECE.
I personally would just tell them that while you don't have it, your experience and research has helped you to form a really awesome program that you feel works for the children in your care.
As with anything in life, an education is good to have, but life experience is just as valuable. There are those with ECEs, teaching degrees etc... who should not be around children as they just do not have what it takes to "handle" them properly, and then there are those who do not have any formal teachings but intrinsically know what children need and have a natural ability to be a great teacher/provider.
I hope what I am saying makes sense. I would just be honest and upfront and if they like you, they will sign on.