Hi Jean... it looks as if I posted to the wrong entry, one of DJDouglass... it's been awhile since I was on this website, so I got confused.
Anyway, I've copied and am pasting what I wrote into this message:

Thank you, Jean, for the response to my November 2006 inquiry. No, I had no more information since then, and your information is right on the money. YES, the names of the children, for the most part, do match the names in the Bible. The Bible belonged to Ida Mae Quilliam Descended from Great Uncle William Quilliam. The information is extensive, but I will start with the back of the Family Register page, titled Great Grandfather's Families. There are two lists, one for Quilliam and the other for Cain. The Quilliam list: Philip Quilliam, Samuel Quilliam, William Quilliam, James Quilliam, Elizabeth Quilliam, Mary Quilliam, Margaret Quilliam, Nellie Quilliam, Ann Quilliam
The Cain list: Elizabeth Cain, Nellie Cain, Isabella Cain, Margaret Cain (married James Quilliam), One boy who died young
Other notes on this list:
Their mother's maiden name was Quine
Her Father's name was Daniel
His mother's mainden name was Togman, (which you have suggested might be Taubman)
All of the Isle of Man

This list of children for Quilliam and Togman from the Bible then are:
Philip, Samuel, William, James, Elizabeth,
Mary, Margaret, Nellie, Ann
They compare with about three differences or exceptions with the list you provided of Christenings for the children of James Quilliam and Elenor Taubman... from your list:
Philip 1788, Samuel 1791, Margaret 1795, Ann 1797, Mary 1799, (you don't have William 1804, or Elizabeth), James 1806, Elinor 1811 (probably Nellie).
Yes, if you figure about every 2 years for a child, there is space for one between Samuel and Margaret, and space for two between Mary and James, and space for one between James and Elinor.
Since the Bible names William Quilliam as Ida Mae Quilliam's Great Uncle, and then lists him among the comparable siblings including James who married Margaret S Cain, it is very likely that these are the same family.