Hi. I'm sure there's a connection - too many similar names not to be. However, no direct matches:
William Henry Trayling b 1815 Ireland, married to Bridget O'Sullivan, b 1832 (Ireland?). Their children included:
Elizabeth b 1854
Ellen b 1855
William Joseph b 1857
James A. b 1859
John J. b 1864
Albert Francis 1868
Emma 1869
Arthur Joseph b 1871

Please contact me directly at triple.L@shaw.ca if we have a connection. Thanks. Leslie