I'm not a demographer, but I attempted a first order approximation based on what I could find. World-O-Meter has a page with world age structure grouped into buckets of 5 years (eg. 20-24). I roughly calculated the total population over the next 100 years by assuming everyone survives until about age 100, so I just zero out one bucket every 5 years.
Annual emissions are 35.9 Gt CO2, so divided evenly among 7.7 billion people that would be 4.7 tonnes CO2e per person, per year. Assigning those and adding them up gives a total emissions curve like this.
The estimated carbon budget to stay below 2º C is somewhere between 565 Gt CO2 and 1550 Gt CO2. In a no-birth scenario with everything else held steady, we would cross that threshold around 2035 or 2063, respectively.
Even if everyone in the world stopped having children entirely, we would still cruise past the targets to limit global warming to 1.5º or 2.0º. A control on population growth would not, on its own, be a sufficient emissions control measure.
Of course, there is plenty of ways to refine this estimate. More granular age buckets could be used. Populations and emissions factors for different countries could be incorporated. Mortality rates for all age groups could be accounted for. But I'm not a demographer, so I haven't done that.