I had a look on Familysearch.org for you and the only James Pearce of that age I can find was born in Liverpool to Joseph (born c1845) and Louise - they were both born in Douglas Isle of Man but all their children born in Liverpool. Henry c1871, Mary Ellen c1874, and Catherine c1878.
I also found an entry on FreeBMD for a James Pearce born Liverpool - December quarter 1875 volume 8b Page 71.
Hope this helps in your search.