http://catholicism.org/prayer-for-the-conversion-of-non-catholics.html

O Mary, Mother of mercy and Refuge of sinners, we beseech thee, be pleased to look with pitiful eyes upon poor heretics and schismatics. Thou who art the Seat of Wisdom, enlighten the minds that are miserably enfolded in the darkness of ignorance and sin, that they may clearly know that the Holy Catholic and Apostolic Roman Church is the one true Church of Jesus Christ, outside of which neither holiness nor salvation can be found. Finish the work of their conversion by obtaining for them the grace to accept all the truths of our Holy Faith, and to submit themselves to the supreme Roman Pontiff, the Vicar of Jesus Christ on earth; that so, being united with us in the sweet chains of divine charity, there may soon be only one fold under the same one shepherd; and may we all, O glorious Virgin, sing forever with exultation: Rejoice, O Virgin Mary, thou only hast destroyed all heresies in the whole world. Amen.

Hail Mary, three times.
An Indulgence of 500 days (S.C. Prop. of the Faith., Dec. 30, 1868;S.P. Ap., March 18, 1936.  Raccolta No. 579).

I try and say this prayer everyday. I do so specifically for the conversion of non Catholic Americans. I first came across this prayer on the backpage of a Mancipia newsletter, the newsletter that the St. Benedict Center in Richmond, NH publishes.