Hi Laurie,
Trying to trace family and linking them to Irish relatives is diffucult, unless others have their family history done. Judging on the information you have, that you have worked hard on this. The name Byers would be associated with the Ballyjamesduff area and it would be usual for the marriage to take place where the bride was from.
On Roots Ireland there are church records, if your family is Church of Ireland the records are available for
Bailieborough Baptisms1822 - 1873 Marriages 1809 - 1920 & Deaths 1809 - 1920
Billis Baptisms1896 - 1920 Marriages 1851 - 1918 (may include Ballyjamesduff)
For Methodist
Bailieborough Baptisms 1878 - 1919 Marriages 1881 - 1919 No death records
Ballyjamesduff Baptisms 1876 - 1919 Marriages 1886 - 1917 No death records
For Presbyterians
Bailieborough Marriages 1845 - 1920 & Ballyjamesduff & Billasis Baptisms 1826 - 1876
For Catholics the parishes would Killann & Castlerahan
Killann Baptisms 1835 - 1920 Marriages 1835 - 1920
Castlerahan Baptisms 1752 - 1920 Marriages 1751 - 1920 Deaths 1751 - 1868. You could contact the genealogical office in Cavan and see can they help you further they can be reached at Genealogy Centre Contact Details
Irish Family History Foundation
Cana House
Farnham Street
Cavan
Co. Cavan
Email: enquiries@rootsireland.ie
Alternatively you can contact the local paper The Anglo Celt and give them your contact details and ask them to publish your story, if you have photos and can broaden the story out, they may publish it and it may reach someone who has a story about some of their relatives that went to Australia, you never know. Also keep looking for burial records as all the time people are transcribing gravestones and these records are being published.
I hope this is of some use to you.
Best Wishes Carmel O'Callaghan
