Think about it. The Annunciation is the moment of his conception. It was a perfect conception; perfect in love, perfect in unity, perfect in power and purity. Our own conception may have been less than the best. Maybe at that very first moment of life we were somehow tainted with lust or drunkenness or inability to love fully or some human flaw in the circumstances or in our parents. It might have left a wound or an empty place in our lives. The mystery of the Annunciation can be the point in the Rosary where we connect with that greater grace which will heal that broken-ness.
The Visitation is the time when Christ was in the womb of the Blessed Mother. It was a time for him of perfect bliss, perfect love and growth in perfection because he had a perfect Mother. In our own lives those nine months may have been stressful for all sorts of reasons. Maybe we weren't really wanted. Maybe mother was sick. Maybe there was stress in the family. That stress can be communicated and maybe those nine months for us were a time when a foundation of fear or stress or lack of love were established. Praying the second joyful mystery helps to bring God's perfect love into our lives.
The same principle applies to the other mysteries of the rosary. This is the theme and method of my book Praying the Rosary for Inner Healing. This has been by far the most popular of all my books, with people from around the world writing to me to say how it has changed their lives. They tell me how they have got extra copies to give to others, and it has been a surprising and joyful thing to see how it has been used by God.
Bl. John Paul II said that the rosary connects with every stage of human life, and so it is. In a mysterious way we identify and put our imperfect lives into the perfect life of love between Christ and his mother. It is no mistake that we call the events of the rosary 'mysteries' for they work in the world and work on us in a mysterious way--because a mystery is something that can be experienced even if it cannot be explained.