Looking at Griffiths valuation, we find in various years between 1852-1864
Cosker living in Co Carlow, Co Down 1864 Tullylish, Co Fermanagh, Co Londonderry, Co Tyrone Co Wicklow, Co Wexford
McCosker living in Co Antrim, Tens live in Co Down inc Tullylish and other Co Down areas.etc etc. However the vast majority are living in Co Fermanagh and Co Tyrone.
Looking at census of Ireland in 1901 the only people living in Ireland relevant
Cosker lived in Co Wicklow, Coolboy district, Hillbrook Lower townland.
McCosker lived in Co Donegal, Raphoe and Clonleigh South ie Lifford, Co Tipperary, Killavinoge district, Co Tyrone, , in Strabane. one in Waterford,
By 1911, they no longer lived in Co Tipperary, or in Co Tyrone
So you your mischance of going onto the Co Down board has paid dividends after all. However the McCosker who vanished, or who experienced a drop in population from the north of Ireland are significant. The period appears to be mostly between 1864 and 1901. I hope you find the reason.
Anyway you have along way to go, but don’t give up keep looking at all the Griffiths Valuation and possible an uncommon first name coming through time might give you a clue where to look earlier.
Good luck , JimG
PS the website is
http://www.askaboutireland.ie/griffith-valuation/index