This article describes a dataset of total (spectrally-integrated rather than wavelength-dependent) emissivity values pertaining to gaseous media containing carbon dioxide (CO2) and/or water vapor (H2O) with the sum of their partial pressures being near the atmospheric level. These conditions may be particularly relevant to flue gases resulting from oxy-fuel combustion. The emissivities here are computed using the EM2C implementations of the statistical narrow band (SNB), and they are made conveniently available as 10 separate plain text files having a unified layout. Each data file in the dataset corresponds to a specific chemical composition (from pure CO2 to pure H2O), with eight intermediate H2O:CO2 molar ratios being 1:20, 1:8, 1:4, 1:2, 1:1, 2:1, 5:1, and 20:1. In addition, pure CO2 corresponds to the extreme lower-bound for the H2O:CO2 molar (as 0:1), and pure H2O corresponds to the extreme upper-bound for the H2O:CO2 molar ratio (1:0 or infinity). For each chemical composition, the total emissivity values are provided for different pressure-pathlengths and different absolute gas temperatures as two independent variables. The pressure-pathlength range spans about three orders of magnitude, from 0.01 atm.m to 50 atm.m, with 90 nonuniformly-distributed pressure-pathlength values. The absolute gas temperature spans a wide range from 300 K (room temperature) to 2900 K (high-temperature flames) with a uniform step of 25 K separating 105 temperature values. For each data file, there are 90 x 105 (9450) emissivity values; and the entire dataset contains 94500 emissivity values.