Cuprate superconductors host a multitude of low-energy optical phonons. Using time-and angle-resolved photoemission spectroscopy, we study coherent phonons in Bi2Sr2Ca0.92Y0.08Cu2O8+δ. Sub-meV modulations of the electronic band structure are observed at frequencies of 3.94±0.01 and 5.59±0.06 THz. For the dominant mode at 3.94 THz, the amplitude of the band energy oscillation weakly increases as a function of momentum away from the node. Theoretical calculations allow identifying the observed modes as CuO2-derived A1g phonons. The Bi-and Sr-derived A1g modes which dominate Raman spectra in the relevant frequency range are absent in our measurements. This highlights the mode selectivity for phonons coupled to the near-Fermi-level electrons, which originate from CuO2 planes and dictate thermodynamic properties.