Is it good to Pray the Rosary daily with the intention of the conversion of the sinner?

Yes, daily praying of the Rosary for the intention of the conversion of sinners is considered an excellent and highly encouraged practice within the Catholic Church. This devotion is strongly supported by Church teaching, numerous popes, and the messages of Marian apparitions like Our Lady of Fatima. 

The Catholic Perspective

• A Specific Request from Mary: During the recognized apparitions at Fatima in 1917, the Blessed Virgin Mary repeatedly stressed the critical importance of praying the Rosary daily for the conversion of sinners and for world peace. She requested that the "O My Jesus" prayer be added at the end of each decade: "O My Jesus, forgive us our sins, save us from the fires of Hell, lead all souls to Heaven, especially those in most need of Thy mercy".

• A Powerful Weapon: Many saints and popes have referred to the Rosary as a powerful spiritual weapon against evil, sin, and the devil's influence. Praying it for the conversion of sinners is seen as a direct way to engage in spiritual combat and obtain graces for those in spiritual danger.

• An Act of Mercy and Charity: Intercessory prayer for others, especially for sinners to turn back to God, is a profound act of Christian charity. The belief is that through the Rosary, Mary intercedes with her Son, Jesus, to grant the necessary graces for repentance and salvation.

• Spiritual Benefits: Beyond helping others, this practice benefits the person praying by increasing their own holiness, fostering a deeper relationship with God, and helping them to overcome personal sin. St. Louis de Montfort famously said that a person who faithfully prays the Rosary every day will eventually give up sin or give up the Rosary, indicating its transformative power. 

In summary, this specific daily prayer intention is a deeply valued and recommended devotion, believed to be highly effective for the spiritual well-being of both the person praying and the sinners for whom they intercede. 

These sites detail how praying the Rosary daily for the conversion of sinners is a central devotion in Catholic spirituality, supported by popes and saints.