Currently being a freeloader, I'm apparently not allowed to send a message!
In addition to the children you list, there was a Charles between James and William. He was baptised 26/06/1831 in St Peter's Church, I presume he died before the 1841 census. You listed the children in birth order, except Mary Ann came before William, rather than after. I have to ask - was there another Mary Ann? The one I have was baptised 06/01/1837.
I'm descended from William Eivers' daughter Sarah, so we're both from his first marriage. Are you aware of the untimely death of Catherine Doherty, the mother?