I found one study from 2017 that says (emphasis mine):
We recommend four widely applicable high-impact (i.e. low emissions) actions with the potential to contribute to systemic change and substantially reduce annual personal emissions: having one fewer child (an average for developed countries of 58.6 tonnes CO2-equivalent (tCO2e) emission reductions per year), living car-free (2.4 tCO2e saved per year), avoiding airplane travel (1.6 tCO2e saved per roundtrip transatlantic flight) and eating a plant-based diet (0.8 tCO2e saved per year).
All the recent conversations around this seem to link back to this one study. This seems like a pretty important issue on which there should be plenty of research. Are there other scientific studies estimating the impact on climate change of having a child today?