Having read many of these responses, including "not short flings" and "date 7 when sex comes up", and my suggestion would be a bit of a reversal.
Instead of telling people what you don't want, wait a few dates, to see if the relationship means anything at all. I don't know your personality or culture, but from American culture relationships typically progress to kissing at least one date before progressing to intercourse, so perhaps wait to see if that feels compatible.
Then talk about what you DO want: A mate that will never want to have children, is fine growing old without them. Be honest but vague (as you were with us); just that, although you are capable of pregnancy, various issues make you fearful of the outcome and you never will get pregnant (and perhaps will terminate if that happens by accident) and you will not adopt.
So you are looking for a mate of like mind. Now that you know after a few dates the relationship between you could go further, you want to clarify some issues before you get your hopes up, and before the relationship becomes a more serious affair.
Warn them, kindly, that if they swear they do not want kids, then later change their mind, that ends the relationship, married or not: Because in your mind and about something this important to you, lying now would be a transgression you cannot forgive.
Added by request of comment: Why this approach is a good idea.
(I will note that I gave my own daughter all of this same advice at 17.)
1) Why wait a few dates? One is psychological (for your date). Think of the date as analogous to a mutual sales process, even though what you intend to exchange is not cash, you are exploring the value of a trade of mutual affection. (And this is just an analogy, I am not suggesting either side is prostituting themselves!)
In sales, we are taught to invest time with a prospect before we start springing the prices and contracts upon them. If you do that too early, they balk, because (a) they have invested very little time or attention so far and have little to lose, (b) they know almost nothing about the product other than what it looks like, so they have no "features" in mind that they covet, and (c) in their mind, knowing nothing, outside of appearance the product is nothing special and perfectly average, and there are likely other products with appearance that appeals to them too: Thus if the price is rather high or the contract has unexpected demands, those extra costs appear onerous and they say "thanks, but no thanks, I'm still looking."
This is basic human psychology you should recognize from being sold anything.
Applied to romance (for either men or women), a contract requirement of "no children ever" is a higher price for a suitor to pay. But there is a segment of the suitor population for whom this extra price in the relationship would be tolerable, because their goal is not to find a womb for their children, but to end their loneliness and a shallow existence, to find mutual love and companionship, have a regular sex life that isn't a series of couplings with virtual strangers, and feel secure in a life partnership that won't stumble and fall or suffer alone when misfortunes strike. Be they financial, health, or the loss of friends or family.
However, you have a better chance of finding a suitor that will PAY this price AFTER they have been exposed to the unique features of what they gain: Your personality, humor, politics, the movies or TV shows you like, the books you like, the sports you like to watch or participate in, and what your quirks are: Are you messy? Neat? Meticulous? Do you live on a tight schedule or not? Are you aggressive in asserting what you want, or avoid confrontation?
Note that there are no right answers to any of that, different suitors may like different sides of the same coin in every instance, or be at different points on the scale. Further, you are evaluating their "product" (their personality) on all the same criteria.
I say wait until the first kiss because by then, you should know whether this is a guy you want, and whether you are a girl he wants as more than a sexual conquest. In other words, don't try the kiss if you aren't already happy spending time with him. I should add in particular, spending time on free or very low expense excursions: Cooking together, watching television together, playing games of some sort. Because men will spend five times more than they can continue to afford wooing a women, so if what you enjoy is meals in a restaurant that cost half a week's pay, that doesn't count. Expensive dates will not continue indefinitely and likely won't last half a year.
Your exploration is for the long haul. So if (like my spouse and I) you both enjoy local amateur stage plays for beginning actors, and the tickets are less than an hour's wages, that is fine. If you both enjoy watching murder mysteries on television, fine. If what melted your heart was the vacation that cost him a month's pay, put it aside and concentrate on things that will plausibly be a regular part of your life.
Again, I told my own daughter all of this: If you date with the intent of revealing the real you and discovering the real him, then before the first kiss you should have rejected him (for any reason you discover along the way, whether it relates to kids, drugs, alcohol or bigotry), or accepted him for his personality and know he is interested in you for your personality. Your kissing and any other pre-intercourse physical interactions are, besides having fun, also a discovery and time to talk about more intimate details of sexual compatibility, likes and dislikes, and sexual history. (As I advised my daughter, one does not have to be naked to bring this topic up, and if you cannot bring yourself to do it, it is probably too early in your relationship to be physically engaged at all.)
For you, if both non-sexual and sexual compatibility seem likely, this is also the time to bring up the intimate detail of not having children, before intercourse begins. Perhaps not while you are kissing, but in a frank conversation in a different and perhaps more neutral and less emotionally charged setting. He knows enough about you to decide if the price of "no kids" matters to him or is something he is willing to sacrifice. You know enough about him to probably predict his answer, even before the first kiss, and know if you want him as a partner.
All of this is made possible by the fact that you do not want short flings and you require several dates (7) before "sex comes up." I agree with that more guarded approach. My suggestion is use that time for a more planned approach to discovering what you need to know. I firmly believe the reason we can reason is to better our long term emotional lives, and you should have no qualms in being analytic and thorough in discovering whether a guy is a short term infatuation or a life partner.
2) Why tell him what you want: What YOU want in a mate is not really arguable by him, and psychologically doesn't sound like a demand for sacrifice or an ultimatum to comply. It sounds like a quality he either has or does not. It is less offensive. In sales, saying "We can only entertain offers from owners of established businesses", it sounds less rude and haughty than saying "Establish your business and get back to us." Yes, they are basically equivalent statements. But how you phrase it can soften it while still delivering the same information. In a way, this is a form of "It's not your fault, it's mine." (Without calling it a 'fault'.) It is truly a part of your personality that your suitor needs to know, a quality you require before you leave the border of "friends" and enter the land of "lovers".
3) Why warn them. This is to raise the stakes and be honest with them and not waste their time. You don't want to hurt them, and you don't want them to hurt you. Intercourse is far more intimate (for most) than kissing or other pre-intercourse sexual activity, there is a reason most of us consider it the consummation of a romantic relationship, or most of us have some ordered list of increasing weight of physical engagement before any form of actual intercourse. Thus breaking a relationship after intercourse is far more hurtful than breaking a relationship before it.
The warning, preferably while NOT in the heat of passion and without intercourse imminent within the hour, is to give them pause, and carefully and rationally consider whether they should be honest with their friend (you) or lie to your face to get laid. Based on your earlier dates and compatibility, I hope you have already discovered and believe their latter option (lying) is highly unlikely, so you will get the truth, and recognize it, instead of a deception. Getting the truth at this point is far more likely if you are fond friends than if you are strangers. The stakes matter, you feel like they care about your feelings, you feel like they value you for more than just your appearance or sexual attributes.
Those are the benefits of this approach. My last piece of advice would be to sustain an element of doubt in your mind, as long as there remain unanswered questions. There is nothing wrong with feeling infatuated or excited or even lustful, but always remember you are in a discovery in progress. Don't fall in love until you feel sure you will not fall alone.