You didn't mention in your question posted on the FamilyHistory message board where your Coffee ancestors may have come from in Ireland.
But see the entry below about the name. The information is taken from a book by Edward MacLysaght entitled "Irish Families: Their Names, Arms And Origins."
In Irish this name is O Cobhthaigh, pronounced O'Coffey as in English: it is probably derived from the word cobhtach, meaning victorious. Coffey is one of those surnames which have not resumed the prefix O, dropped during the period of Gaelic submergence. Several distinct septs were prominent in mediaeval times, of which two are still well represented in their original homeland. These are O'Coffey or Corcalaoidhe in south-west Co. Cork, where local pronunciation often makes the name Cowhig or Cowhey, as in the place name Dunocowhey, called after them. This sept is of the same stock as the O'Driscolls. A second minor sept was a branch of the O'Maddens of Ui Maine, whose descendants are fund to-day in Co. Roscommon. A third, once of considerable importance but now scattered, belonged to Co. Westmeath where they were famous as a bardic family. The most distinguished of these was Dermot O'Coffey (fl. 1580), the Gaelic poet. Six other poets of this family are represented in Gaelic literature. In more recent times the Leinster Coffeys are represented by Charles Coffey (1700-1745), dramatist and actor, the first to introduce Irish airs in a play. George Coffey (1857-1916), the archaeologist, though his family has long associations with Dublin, was descended from the Munster sept. The place-name Rathcoffey occurs both in Co. Kildare and Co. Leix.