There was a Jeremiah Conner in the Exeter, NH area as early as the 1660s. That wouldn't be the one you are specifically looking for, but could be one of his ancestors.

Many people are not aware that a sizeable number of Irish youth were kidnapped and forcibly carried to America in the mid 17th century, where they were sold as servants without indentures. Most went to Virginia and the Caribbean islands, but a few hundred of them ended up in Massachusetts. I discovered this some years ago while researching the roots of my Lary ancestors. Conners and Larys, as well as Kellys, Driscos and Cartys (all Irish surnames corrupted into an English variation) can be found very early in Exeter, later spreading into southern Maine and northern NH. Not all the Irish came to America in the 18th and 19th centuries. Some were here much earlier.

While I have no specific knowledge of the Conners, besides the references I ran across in researching the Larys, I think it would be worth your while to check out this possibility.

If you want to correspond further about this, write me off the board at franzm@flash.net