Hi --
I found the following births for children of James & Ellen Biggane in Co. Limerick on the Dalton Data Bank:
4 May 1866, Anne Dalton born to James Dalton & Ellen Biggane at Athea, Newcastle RD (Registration District), Co. Limerick
22 Feb 1869, Ellen Dalton born to James Dalton, stone mason & Ellen Biggane at Glenagower, Newcastle RD, Co. Limerick
22 June 1871, James Dalton born to James Dalton, stone mason & Ellen Biggane at Gortnagross, Rathronan, Newcastle RD, C. Limerick
9 Apr 1877, Johanna Dalton born to James Dalton & Ellen Biggane at Athea, Newcastle RD, Co. Limerick
You can check the Dalton Data Bank at
http://www.daltondatabank.org/ -- it contains transcriptions of over 300,000 records of Daltons world-wide.
Hope this helps,
--Karen Dalton Preston