Interlayer coupling plays a critical role in van der Waals materials by governing lattice stability and emergent quantum phases, yet its impact on few-layer hexagonal CoTe₂ remains unclear. Here, using first-principles calculations, we systematically investigate monolayer and bilayer CoTe₂ with an emphasis on their electronic structures, lattice dynamics, and electron-phonon coupling, and elucidate the underlying mechanisms driven by interlayer interactions. Our results show that monolayer CoTe₂ exhibits pronounced dynamical instability at low temperatures, whereas interlayer coupling stabilizes the bilayer crystal structure and gives rise to phonon-mediated superconductivity with a predicted critical temperature of about 4.7~K when spin-orbit coupling is included. The stabilization and superconductivity in bilayer CoTe₂ are primarily attributed to interlayer-coupling-induced Te-p_z charge redistribution and the associated modification of the Fermi surface and electron-phonon coupling. Finally, we discuss how spin-orbit coupling in bilayer CoTe₂ weakens the EPC and superconductivity. Our work clarifies how interlayer coupling can jointly tune structural stability and superconductivity in few-layer CoTe₂, providing insights for engineering quantum phases in layered transition-metal dichalcogenides.