I found a record in the civil registration of births for Jeremiah Hanlon, born 21 April 1869 in registrar's district of Ardfert, superintendants' district of Tralee, which covers Bellyheige. Father's name is given as Patrick Hanlon of Doonamontane, located in civil parish Ballyheige. Mother's name is Mary, formerly Biglan or Reglan.
Then found marriage record for Patrick Hanlon of Doonamontane and Mary Regan for 25 Feb 1868. Then found 10 Apr 1869 baptism record for Jeremiah, with parents Patrick and mother Mary Regan at Ballyheige Roman Catholic Parish. Sponsors were Hanora and Nicholas Regan. The same named parents appear to have daugthers Honora baptised 1877, Johanna baptised 1874. Found Patrick Hanlon living next to Regan's in Griffith's Tiershanagan, Ballyheige.
Hope this is useful and hoping also to see if Jeremiah's parents might have been related to a John Hanlon (b about 1800) or his son Daniel born 1828.