You have a great story already to help you with this - you've ended dating relationships due to your desire to not have kids. When the issue arises or when you start it, you can add
TOPIC OF CHILDREN STARTS
I don't want children and I've ended a few dating relationships where I really liked the person (if true) because they wanted kids and I did not. I liked them a lot (if true), but this isn't a position I'm willing to change ever.
That sends a clear message. If someone thinks they can change your mind, I don't think any message is going to get through to them.
On this point:
So far, the record is 6 dates before the date will inevitably say something along the lines of ...
I did miss this - "record" as in the latest date they mention it or the earliest date they mention it? To avoid dating a long period before having this conversation, bring it up as early as it makes sense. Any topic related to children can easily be directed to a conversation about not having kids ever. Same with future, such as "I've always seen myself as ..." Make sure to add that you've ended relationships because of this when people tried to change you or thought that you would change.
