What support is there in the Patristic writings for Marian Devotion? Specifically, I want to know if there is evidence in the early Church of Christians venerating Mary.  Evidence from the time following Mary's earthly life is preferred, though not required.
As has been mentioned in answers to other questions, the prayer Sub tuum praesidium appeared around 250. It was originally written in Greek.


  Ὑπὸ τὴν σὴν εὐσπλαγχνίαν,
  καταφεύγομεν, Θεοτόκε.
  Τὰς ἡμῶν ἱκεσίας, μὴ παρίδῃς ἐν περιστάσει,
  ἀλλ᾽ ἐκ κινδύνων λύτρωσαι ἡμᾶς,
  μόνη Ἁγνή, μόνη εὐλογημένη. 
  
  Beneath your compassion,
  We take refuge, O Mother of God:
  do not despise our petitions in time of trouble:
  but rescue us from dangers,
  only pure, only blessed one.


Dr Mark Miravalle of the Franciscan University of Steubenville has written an entire book on the subject, Introduction to Mary: The Heart of Marian Doctrine and Devotion [Queenship 2006], a summary of which &mdash; with references &mdash; is available from piercedhearts.org. He mentions St&nbsp;Ambrose (d. 397) calling Mary "Mother of Salvation".

He goes on


  The Christian witness of the first centuries of the Church also provides us with examples of direct prayer to Mary as a means of intercession to the graces and the protection of her Son.
  
  For St Irenaeus, Mary is an "Advocate," or interceding helper, for Eve and for her salvation. St.&nbsp;Gregory Thaumaturgis (d.350) depicts Mary interceding for those on earth from her position in Heaven.
  
  St Ephraem (d.373), the great Eastern doctor and deacon, directly addresses the Blessed Virgin in several Marian sermons. Direct prayer to Mary is also found in a sermon of the great Eastern Father, St&nbsp;Gregory Nazianzen (330-389). By the last part of the fourth century and the beginning of the fifth, we have numerous explicit examples of direct prayer to the Mother of God, for example in the writings of St&nbsp;Ambrose, as well as by St&nbsp;Epiphanius.