Photonic platforms with χ^(2) nonlinearity offer new degrees of freedom for Kerr frequency comb development. Here, we demonstrate Kerr soliton generation at 1550?nm with phase-matched quadratic coupling to the 775?nm harmonic band in a single AlN microring and thus the formation of dual-band mode-locked combs. In the strong quadratic coupling regime where the χ^(2) phase-matching window overlaps the pump mode, the pump-to-harmonic-comb conversion efficiency is optimized. However, the strong quadratic coupling also drastically modifies the Kerr comb generation dynamics and decreases the probability of soliton generation. By engineering the χ^(2) phase-matching wavelength, we are able to achieve a balance between high conversion efficiency and high soliton formation rate under the available pump power and microring quality factors. Our numerical simulations confirm the experimental observations. These findings provide guidance on tailoring single-cavity dual-band coherent comb sources.