Long story short: Mary became Molly, due to the difficulty some dialects have with the letter R. Rhyming nicknames were all the rage back in Ye Olde English (Rick-->Dick, Will-->Bill, etc), so Molly became Polly.
However, Polly's not exactly an intuitive nickname for Mary in modern English, so here're some alternatives. :)
- Apolline (ah-pol-leen, French)--form of Apollonia. Other variants include Apolena (Czech), Polina (Russian), and Polona (Slovene).
- Palmira (pahl-MEE-rah, Italian, Portuguese, Spanish)--"traveller"
- Paloma (pahl-OH-mah, Spanish)--"dove"
- Paolina (pow-LEE-nah, Italian)--feminine form of Paul, "humble"
- Penelope (pen-EL-oh-pee, Greek)
- Peronel (PEHR-oh-nel, English)--form of Petronilla
- Polymnia (pol-IM-nee-ah, Greek)--"many songs". The Greek muse of dance & song.
- Polyxena (pol-ih-KSEE-nah, Greek)--"much hospitality"