I believe the answer to this serious problem is that, as overpopulation becomes a problem, people will realize that they are unable to care for any children they have. In the face of such a situation, where having children would be wrong due to it being impossible to care for them, people will have to choose between celibacy and doing wrong.
The ‘Catholic way’ in that scenario would be to stay single. If you aren’t capable of raising children, then I think it’s safe to say that God isn’t calling you to married life.
Of course, in reality, most people would likely choose some some road which is not the ‘Catholic way’.