That should be pretty obvious from a libertarian point of view. If a person has a right to have children, then somebody else has an obligation to make sure he can exercise that right. But nobody has that obligation: nobody is obliged to become your wife. If you were, say, a prisoner in a state penitentiary, the state wouldn't be obliged to supply you with a concubine so you could have childen. Hence, you do not have a "right" to have children.
What any ordinary person has, is the right to seek marriage with a spouse who, via sexual union, may be able to jointly procreate with you.
As for a right to exist--- I don't know what to make of that. If a person has already begun his existence --- that is, if he has already been begotten --- he has the right to be nurtured and cared for by his parents. If no such person exists, then a "right" cannot exist.
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Mrs. Don-o, you are on a tear today. Excellent.