"Collincy" is near certain to be the Irish townland involved.
The townland is a peculiarly Irish concept which has survived to the present day.
Basically, it's an administrative unit at the level below the parish.
Think of the many Scottish placenames ending in "ton" or "toun", - Fermtoun [of], Millton [of], and many, many other such Scottish placenames of the form "....ton" and ".....toun". These are the precise equivalent of the Irish townlands, but never gained the same recognition in terms of local government as was the case with the townland in Ireland.
There are many, many websites that a Google will produce that list the 1,000s of Irish townlands.
The ever present problem is the spelling of the townland name, so that you may need to use your imagination to recognise that a certain townland in Co. Sligo, given the historial Erse (Irish Gaelic) spellings that will indubitally occur, compared to the "Collincy" spelling that you have come across

, - so think in phonetic terms (and ask a mate who understands Irish Gaelic pronunciations, as the spoken quite often is quite difficult to relate to the written!).
Incidentally, given the need for a miller or even millers in every townland, - it was impractical to consider transporting the grain over more then local distances, - I'd be surprised if a miller moved very far, unless there were very strong reasons to do so, - and these could well be family related.....
David