For frequency of Erin:
http://www.behindthename.com/php/search.php?terms=erin&gender=f&extra=p
For frequency of Eryn:
http://www.behindthename.com/php/search.php?terms=erin&gender=f&extra=p
Sorry, this site doesn't list the frequency of usage for Eryne -- most likely due to the fact that it's a rare variation of the name Erin.
Because the name Erin is representative of Ireland
http://www.behindthename.com/php/search.php?terms=eireann
...and also springs from Irish legend
http://www.crosswinds.net/~daire/names/celtirishfem.html
...I doubt that there were any saints named Erin to qualify a feast day for the name. I could be wrong, however, and you may want to search a few Catholic websites which list saints and their feast days.
-- Nanaea