"...keep the commandments of God, that they might rejoice and be filled with love towards God and all men," Mosiah 2:4.
One of the rewards of keeping the commandments is being filled with joy and love. Is this a possible cure for melancholy? I testify from experience that faith, repentance, loving one's neighbors, charity, service, and so forth bring peace, joy, and love. One can't be depressed while being buoyed up with these.