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Using time- and angle-resolved photoemission spectroscopy, we study coherent phonons in Bi$_{2}$Sr$_{2}$Ca$_{0.92}$Y$_{0.08}$Cu$_{2}$O$_{8+\\delta}$. Sub-meV modulations of the electronic band structure are observed at frequencies of $3.94\\pm 0.01$ and $5.59\\pm 0.06$ 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 CuO$_{2}$-derived $A_{1g}$ phonons. 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