The physical properties and structural evolution of the 122-type solid solution BaNi₂(Ge_1−xP_x)₂ are reported. The in-plane X-X (X = Ge_1−xP_x) dimer formation present in the end member BaNi₂Ge₂, which results in a structural transition to orthorhombic symmetry, is completely suppressed to zero temperature on P substitution near x = 0.7, and a dome-shaped superconducting phase with a maximum T_c = 2.9 K emerges. Clear indications of phonon softening and enhanced electron-phonon coupling are observed at the composition of the structural instability. Our findings show that dimer breaking offers possibilities as a tuning parameter of superconductivity.