Most modern rockets run on liquid oxygen and liquid hydrogen which reacts to water vapor. There is no carbon in this reaction, so the carbon-monoxide and carbon-dioxide output of the reaction is zero.
Regarding the CO2 footprint of the production of liquid oxygen and liquid hydrogen: These are made by splitting water into oxygen and hydrogen through electrolysis and then compressing it. There are different methods to do this, but all of them need more or less of electric energy. The CO2 footprint depends vastly on how this energy is created. When you use energy from regenerative resources or nuclear energy, it would be possible to have a completely CO2-neutral rocket launch.
Some other ways to split water into its constituent components (hydrogen as fuel and oxygen as oxidizer) are direct solar water splitting process in which the solar energy is directly used to produce hydrogen from water without going through the intermediate electrolysis step:
- Photoelectrochemical water splitting – this technique uses semiconducting electrodes in a photoelectrochemical cell to convert light energy into chemical energy of hydrogen. There are essentially two types of photoelectrochemical systems – one using semiconductors or dyes and another using dissolved metal complexes.
- Photobiological – these involve the generation of hydrogen from biological systems using sunlight. Certain algae and bacteria can produce hydrogen under suitable conditions. Pigments in algae absorb solar energy, and enzymes in the cell act as catalysts to split water into its hydrogen and oxygen constituents.
- High temperature thermochemical cycles – these cycles utilize solar heat to produce hydrogen by water splitting using thermochemical steps.
- Biomass gasification – this uses heat to convert biomass into a synthetic gas rich In hydrogen.
None of these require additional electric energy and their carbon emissions are zero. This does not include any electricity used for compression and cooling of cryogenic Lox/LH2 propellants. In case of using electrolysis though, by using the lower heating value of hydrogen, the electrical energy needed to generate one kg of hydrogen is 51 kWh, assuming electrolyzer efficiency of 65%.
But there are still some older designs in use where the first or even all stages run on liquid oxygen and kerosene, like the Russian Soyuz which supply the ISS. Kerosene has a CO2 footprint of about 2.5 kg per liter. A Soyuz-2 burns about 82 tons of kerosene per launch. With RP-1 fuel density at 0.81–1.02 g/ml, this comes out roughly between 67-84 tons of CO2 per Soyuz 2-1B (using 4 boosters) launch.