The surface tension of water is decreased by CO2 and levels off at higher pressure. The determination of interfacial tension in these systems is, however, not so easy to measure and there may be discrepancies between different experiments. There are references to relevant literature in these articles:

https://egel.kaust.edu.sa/Documents/Papers/Espinoza_2010c.pdf

https://www.osti.gov/servlets/purl/1183177

This second paper gives some data which the authors have selected as being the most reliable.

Is there any generalized formula using which we could calculate the surface tension of binary mixtures containing water? I am simulating the problem of a bubble rising in ANSYS. Hence, I need the surface tension coefficients for different mixtures.

Dennis is right. Most experiments are done in pressure cells. There is no generalized formula or empirical relation to calculate IFT of binary mixtures with one species being water. Here is a literature that lists quite a few binary mixtures of H2O (see Table 1). I hope this helps.

Measurements and Modeling of Interfacial Tension for CO2/CH4/Brine Systems under Reservoir Conditions

Yueliang Liu, Huazhou Andy Li, and Ryosuke Okuno Industrial & Engineering Chemistry Research 2016 55 (48),12358-12375

DOI: 10.1021/acs.iecr.6b02446