The parent is looking for reassurance so give them examples of how you manage. To just say you are good at your job and through years of experience you have the skills to manage is not giving any specifics and could easily be interpreted as somewhat arrogant and big headed especially if you aren't going to back it up. They don't know you from Jack, so why should they take you at your word without it being backed up. Trust comes with time I appreciate that but this is their child we are talking about. No room for error when finding a caregiver you are happy and comfortable with.
There are also a lot of providers who have been doing this job for years who totally suck and are pretty crappy providers but go unnoticed. They have nice daycare rooms, good credentials and years of experience but once that door closes, who knows what REALLY goes on. I don't think it's to much to ask from a parent as to how we cope with so many little ones. A new parent is going to have lots of questions and sometimes needs more reassurance.It doesnt mean they will be a bad client but perhaps they are a little more anxious than others at first or have heard horror stories and just need that extra bit of reassurance. If you asked them how they managed their job, I'm sure they wouldn't think twice about telling you how they do it, and I am confident they wouldn't judge you or think badly of you for questioning them.
This is their child we are talking about and after 1 or 2 meetings with you they really don't know you so if a little reassurance is what they need, give it to them. It will just be furthur afirmation that you are a kind and caring daycare provider who has respect for them and their situation when it comes to looking for a provider who they feel 100% happy with. If you trivialize their concern, it's only a bad reflection on you.