Throughout his life he wrote on prayer, usually tersely, though occasionally he wrote at length, as when he proposed some changes to the Episcopal Church's Book of Common Prayer based on his semeiotic theory.
Here is one piece from his journal, written while he was a student at Harvard in 1859. It appears to be a re-writing of the Lord's Prayer:
"I pray thee, O Father, to help me regard my innate ideas as objectively valid. I would like to live as purely in accordance with thy laws as inert matter does with nature's. May I, at last, have no thoughts but thine, no wishes but thine, no will but thine. Grant me, O God, health, valor, and strength. Forgive the misuse, pray of thy former good gifts, as I do the ingratitude of my friends. Pity my weakness and deliver me, O Lord; deliver me and support me."
(This is from MS 891, “Private Thoughts,” number XLVI. Peirce's writings include his vast unpublished writings, mostly held at Harvard, with copies at IUPUI and Texas Tech)