Let's not forget that St. Joseph, the most chaste spouse of the Blessed Virgin Mary, is the Patron of the Universal Church. His Solemnity, which in the United States, oddly, is not a holy day of obligation, is 19 March. It is customary to pray a Novena in the days leading up to 19 March. Since Novenas, as the name indicates, are 9 days, we begin on 11 March, which is perfect for the Conclave.
Here is the Novena prayer, the prayer we pray each day of the 9 days:
Saint Joseph, you are the faithful protector and intercessor of all who love and venerate you. I have special confidence in you. You are powerful with God and will never abandon your faithful servants. I humbly invoke you and commend myself, with all who are dear to me, to your intercession. By the love you have for Jesus and Mary, do not abandon me during life, and assist me at the hour of my death.Let us place first among our intentions we entrust to St. Joseph's intercession the Cardinal electors as they seek the guidance of the Holy Spirit in selecting a new Roman Pontiff.
Glorious Saint Joseph, spouse of the immaculate Virgin, Foster-father of Jesus Christ, obtain for me a pure, humble, and charitable mind, and perfect resignation to the Divine Will. Be my guide, my father, and my model through life that I may merit to die as you did in the arms of Jesus and Mary.
Loving Saint Joseph, faithful follower of Jesus Christ, I raise my heart to you to implore your powerful intercession in obtaining from the Heart of Jesus all the graces necessary for my spiritual and temporal welfare, particularly the grace of a happy death, and the special grace I now implore: (Mention your request). Guardian of the Word Incarnate, I am confident that your prayers on my behalf will be graciously heard before the throne of God