Some additional info following a trip to PRONI;
James Boomer married Eliza Sullivan 10 Aug 1851
Children of James and Eliza
Jane Boomer, 31 May 1852 - witnesses Henry Farringham (?) and Jane Boomer (James' sister?)
James Boomer, 14 May 1854 - witnesses John Dorrian and Annie Sullivan (Eliza's sister?)
Brigid Boomer, 30 May 1856 - witnesses William Magennis and Jane Boomer
Catherine Boomer, 11 Sept 1856 - witnesses John Edmonde and

Savage
Roseanne Boomer, 8 Oct 1856 - witness Ann Sullivan
Jane and Catherine, 11 Nov 1865
Brigid, Catherine, Roseanne - all in 1856 doesn't add up. I'm guessing the dates are wrong or it's totally different people. My guess would be that Roseanne is right going by the witness - Ann Sullivan. I know the twins info is right (mother remembers them).
If the earlier Jane is right then I assume she died - was it common to 're-use' names when this happened?
I also found
Philip and Eliza Boomer (nee McDade?) had two children:
Catherine, 18 Sept 1852
Michael 4 may 1855
Maybe ring some new bells :-)
I've found no other Boomers locally - nearest I've found is Donaghadee. Fair way off but maybe connected.
Damien