I did wonder if this Samuel had another first name
in case some of these are unknown to all of you 
http://freepages.genealogy.rootsweb.ancestry.com/~rosdavies/Mr.   James M'CUNNE   .   Comber   of Ballygowan; present as a young boy at the laying of foundation stone for Ballygowan Presbyterian Church 14 Aug 1837   MSch p10
James   McCUNE   .   Killinchy   leased half acre in 1831 from William McCune ; eviction hearing; nilled   RCCPCI p280
William   McCUNE   .   Killinchy   married Elinor Shields 5 Jan 1813 at Killinchy Presbyterian Church   PR
William   McCUNE   .   Killinchy   married Isabella Adair 30 Mar 1829 at Killinchy Presbyterian Church   PR
William   McCUNE/McKUNE   .   
Killinchy & Newtownards   of Ravara; a carpemter; son of William McKune (a carpenter); married Elizabeth Boyd of Mill St, Newtownards 5 Sep 1864 at 4th Presbyterian Church, Newtownards, witnesses were William Gilliland & William Woods ; father of James b. 1868 & Henery b. 1870 & Elizabeth b. 1873; died before May 1884 when Elizabeth remarried   PR;CR
William   McCUNE   .   Killinchy   eldest son of William McCune of Ballydorn ; died 14 Mar 1865 in Jerrysville, Illinois USA   BN 16/5/1865
Tithes Applotment Books 1823-1837 based upon the work of the Irish Genealogy Hub’s index listing for each parish in Northern Ireland,   The relevant original books are in the 
Public Record Office of Northern Ireland (PRONI) Belfast the tithes are a one line record showing acreage of holdings. The records are incomplete and were organised by the Cof I not the state.
McCune, R.   Townland: Ballynoe Year: 1834   Donaghadee   Down
McCune, William   Townland: Drumarkin Year: 1827   Drumballyroney   Down
McCunn, James   Townland: Grallaghgreenon Year: 1827   Drumballyroney   Down
McCune, John   Townland: Ballymagarrick Year: 1829   Drumbo   Down
McCune, James   Townland: Carryduff Year: 1829   Drumbo   Down
McCune, Lawrence     Townland: Carryduff Year: 1829   Drumbo   Down
McCune, Saml.   Townland: Ballydorn Year: 1833   Killinchy   Down
McCune, Wilm.   Townland: Ballydorn Year: 1833   Killinchy   Down
McCune, Saml.   Townland: Ballymacashane Year: 1833   Killinchy   Down
McCune, James   Townland: Ballymacreely Year: 1833   Killinchy   Down
McCune, James   Townland: Ravara Year: 1833   Killinchy   Down
McCune, William   Townland: Ravara Year: 1833   Killinchy   Down
McCune, Samuel   Townland: Ballywoolen Year: 1827   Killyleagh   Down
McCune, John   Townland: Derraboy Year: 1827   Killyleagh   Down
McCune, James   Townland: Killinchy Woods Year: 1827   Killyleagh   Down
McCune, Mr. John   Townland: Lisnaw Year: 1827   Killyleagh   Down
McCune, John, Sr.   Townland: Ballyskeaugh Year: 1833   Newtownards   Down
McCune, James   Townland: Glassdrummond Year: 1834   Saintfield    Down
McCune, Saml.   Townland: Lisbane Year: 1833   Tullynakill    Down
McCune, Wilm.   Townland: Tullynakill Year: 1833   Tullynakill    Down
from  
http://www.dippam.ac.uk/ied/records/46055DEATHS.
McCune - March 14, at Jerrysville, Illinois, America,
  William, eldest son of Mr. Wm. [William?] McCune,
  Ballydorn, Killinchy, [Co. Down?].
(Transcribed by James Tuff.) from belfast newsletter 16-05-1865
tried findmypast migration and castle garden
ggod luck onwards