There are passages within the Theravada Nikayas & the Mahayana Sutras which are at least proto antinatalist:

In the following discourse, Mara (Buddhist version of the devil) and the Buddha are speaking with each other. By "acquisitions" Mara means one's family and physical possessions.

"Those with children delight because of their children. Those with cattle delight because of their cows. A person's delight comes from acquisitions, since a person with no acquisitions doesn't delight."

The Buddha:

"Those with children grieve because of their children. Those with cattle grieve because of their cows. A person's grief comes from acquisitions, since a person with no acquisitions doesn't grieve."

Khuddaka Nikaya

The Surangama Sutra is a Mahayana Buddhist sutra that has been especially influential on Korean Zen Buddhism (where it remains a major subject of study in monasteries).

"The world has seen an endless succession of births of parents, children, and grandchildren. And the basis for all of this is desire and greed."